I've compiled a video list of every Cougar underdog win since 2006, going by game spreads found online.

Each of the entries includes a short video snippet of an important or impressive play from that game.

In total, BYU has won 27 games as an underdog in the last 18 years, starting with . . .

2006 BYU 31 (17) TCU 17
Line: TCU -7
https://www.youtube.com/clip/UgkxhXcnVtvSEZP8762gMLf0otvVnRjYcz_V

The Cougars put an abrupt end to the Horned Frogs' 13-game winning streak. This was BYU's first win over a ranked opponent since 1999.
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2009 (20) BYU 14 (3) Oklahoma 13
Line: Oklahoma -22
https://www.youtube.com/clip/UgkxbldTD8HsED_ucIAQ0tYOzHSAwQmiWkaH

Oklahoma was fresh off a BCS National Championship Game loss to Florida. They Sooners were stacked with Heisman Trophy winner Sam Bradford, future NFL First-Team All-Pro selections Trent Williams, Lane Johnson, Gerald McCoy, and DeMarco Murray, plus future Pro Bowl selection Jermaine Gresham.

BYU was without an injured Harvey Unga, but it didn't matter. Max Hall said they were going to win, and he made good on his word.

It also helped that Coleby Clawson knocked Sam Bradford out of the game (and, unfortunately, out of the season).

This is tied as BYU's largest upset win since 2006.
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2009 (18) Oregon State 20 (14) BYU 44
Line: Oregon State -2.5
https://www.youtube.com/clip/Ugkx_HQOQ_4ikNLD0CXkOYQ3gIdLLZQ33u0K

Looking back, it's pretty insulting that Vegas made BYU an underdog. At 8-4, Oregon State was ranked No. 18. But BYU was ranked No. 14, and also had Max Hall.

Hall skinned the Beavers and completed a 32-7 career record as the starter.
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2010 Washington 17 BYU 23
Line: Washington -1.5
https://www.youtube.com/clip/UgkxwU9-I8n6Lo0JLdny_61U7dU4gldT0PO7

The Cougars opted to cycle through Riley Nelson and Jake Heaps every other offensive series. It actually worked in the season opener against Washington.

Trailing 23-17, Jake Locker led the Huskies to the BYU 27 with under two minutes left. On 4th & 7, Locker basically threw a pass right at defensive tackle Eathyn Manumaleuna, who deflected the ball up and incomplete.
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2010 San Diego State 21 BYU 24
Line: San Diego State -4.5
https://www.youtube.com/clip/UgkxOrENpe2nujh2Sun9tdP20tIojiIrXh4_

This was the game Bronco took over control of the defense. BYU came in with a 1-4 record following a 31-16 loss to Utah State. San Diego State, on the other hand, was coming in at 3-1 after beating Utah State 41-7.

A fake field goal attempt on the Cougars' opening drive led to a touchdown and an early lead. The Aztecs threatened late in the game but the Cougar defense held on for a three-point win.
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2011 BYU 38 Oregon State 28
Line: Oregon State -2.5
https://www.youtube.com/clip/UgkxLFXoY4a8YJZSBsaZaNM5O6u1t5rvpoO0

Another game where Vegas showed little respect for BYU against Oregon State, who came into this game at 1-4.

Riley Nelson threw for 3 touchdowns and led the team in rushing.
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2011 BYU 24 Tulsa 21
Line: Tulsa -2.5
https://www.youtube.com/clip/Ugkx5ybRL_YHsTOPPsv-Al7iOWgtgT9h43db

I'm not sure why an 8-4 Tulsa team was deemed a narrow favorite in the Armed Forces Bowl.

Riley Nelson Dan Marino'd the Cougars to a last-second win.
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2012 BYU 41 Georgia Tech 17
Line: Georgia Tech -2
https://www.youtube.com/clip/UgkxlIHJAqtYyFzKC7uV46LNWApMS-SXl7Hg

Jamaal Williams scored four of BYU's five touchdowns and an elite Cougar defense held Georgia Tech to just 157 yards of total offense.
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2013 (15) Texas 21 BYU 40
Line: Texas -7
https://www.youtube.com/clip/UgkxBR1qR6hLLzfQzuodfd3vL8a7O7ZmVfIs

Pollsters were sooo excited to rank Texas back in the top 15 ("Texas is BACK!") Taysom proceeded to shred the Longhorns so badly, it basically ended Mack Brown's 16-year tenure as Texas head coach.
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2013 BYU 31 Utah State 14
Line: Utah State -6
https://www.youtube.com/clip/UgkxyiJhIyspAxjE7z1eobLwLrLxMEW2ZFFd

Kyle Van Noy picked off Chuckie Keeton and returned it for a touchdown on the first play from scrimmage. It only got worse from there for the Aggies when Keeton tore his ACL while attempting to slip out of a tackle. This one wasn't close.
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2014 BYU 41 Texas 7
Line: Texas -1
https://www.youtube.com/clip/Ugkx1TKtI30CtVAc910HzXgyR8yje6ccYULJ

Pollsters wanted sooo badly to rank Texas in the AP Top 25 ("Texas is BACK!") Coming into this game, the Longhorns received 126 votes, making them the first team outside of the Top 25 rankings.

Then Taysom jumped over a guy, and Texas didn't receive a single vote the entire rest of the year.
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2014 BYU 42 Cal 35
Line: Cal -3
https://www.youtube.com/clip/UgkxBmzXbIaDeRTKG9YmpJdIN7WM1Ol0MIrZ

Christian Stewart had taken over at QB midway through the season after Taysom went down with an injury. Against Cal, Stewart outgunned future No. 1 overall pick Jared Goff by throwing for 433 yards and 5 touchdowns, including the game winner to Jordan Leslie.
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2015 BYU 33 Nebraska 28
Line: Nebraska -5.5
https://www.youtube.com/clip/UgkxsXcMGmkMqAgakjrI_0rjInmQMz3aicvh

Last play of the game, snap Tanner, backpedal, sprintout to the right, he's got time, loads up, launches it, goes for the end zone, the balls in the air, it drops — AT THE GOAL LINE — I THINK HE CAUGHT IT FOR A TOUCHDOWN! HE CAUGHT IT! HE CAUGHT IT! HE CAUGHT IT! TOUCHDOWNMITCHMATHEWS! THE COUGARS WIN IT! THE COUGARS WIN IT!
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2015 (20) Boise State 24 BYU 35
Line: Boise State -2.5
https://www.youtube.com/watch?v=JwmjVwCgB6c

First down and ten Broncos at their own twenty-five yard line, ball between the hashes, Finley shotgun snap, settles, fires, It's INTERCEPTEDDDDDDD!!!! THE COUGARS HAVE IT! KAI NACUA WITH THE HAT TRICK — HIS THIRD PICK — ON THE RUN, THIRTY, TWENTY-FIVE, TWENTY, FIFTEEN, TEN, FIVE, touchDOOOOOOOOOOOWWWWWWWWWWN!!!!!!!!!!!!!!!
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2016 BYU 18 Arizona 16
Line: Arizona -1.5
https://www.youtube.com/clip/Ugkx9yflDIKnIEgB-P_rQjrtM1oDoAjrbuAv

BYU led Arizona for nearly the entire game until the Wildcats grabbed a 1-point lead with 1:26 remaining. Taysom and Jamaal tag-teamed to drive the Cougars down the field and set up Oldroyd for the game winner.
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2016 BYU 31 Michigan State 14
Line: Michigan State -6
https://www.youtube.com/clip/UgkxbZWekkjrX-JFKiatNNs4wdWXVD8e-ps3

A year removed from a trip to the College Football Playoffs, Michigan State had climbed as high as No. 8 early in the 2016 season. Losses to Wisconsin and Indiana dropped the Spartans from the rankings before BYU came into East Lansing.

A Colby Pearson touchdown grab midway through the 3rd sparked a 28-7 second-half run that was more than enough for BYU.
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2017 BYU 31 UNLV 21
Line: UNLV -4.5
https://www.youtube.com/clip/UgkxXeMUD3M0Pny4zSrUvoMe6qMIBnerlY8d

Yes, there was a time when BYU was the underdog against UNLV.

No, UNLV did not win.
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2018 BYU 28 Arizona 23
Line: Arizona -12
https://www.youtube.com/clip/Ugkx8P_f_0szw6dwT2S76vLHH5r3TNZ4XcIm

The 2017 BYU season was so poor that Arizona was a huge 12-point favorite in the 2018 opener. Quarterback Khalil Tate was being hyped as a Heisman favorite, and few believed the Cougar offense was capable of keeping up. But Squally Canada's third touchdown put BYU up 28-10 late in the 3rd quarter.

Arizona would come back to make it close, but BYU ran out the clock for the win.
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2018 BYU 24 (6) Wisconsin 21
Line: Wisconsin -22
https://www.youtube.com/clip/UgkxhUprj2mvDOpUetozsqy1UWnkf6IIVdhQ

Wisconsin had beaten BYU 40-6 in Provo almost one year to the day of this rematch in Madison. BYU showed they were not that same team and beat the Badgers at their own bully-ball game.

This is tied as BYU's largest upset win since 2006.
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2019 BYU 29 Tennessee 26 (2OT)
Line: Tennessee -3.5
https://www.youtube.com/clip/UgkxcNu5vkD4o5waoWDyfRWeGRADhLjQ3wub

The Cougar offense struggled for most of the game until a miraculous last-second catch and run from Micah Simon. BYU had no trouble scoring consecutive touchdowns in the first and second overtime periods.
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2019 (24) USC 27 BYU 30 (OT)
Line: USC -4
https://www.youtube.com/clip/UgkxOUR-SpuTgspZzAKthTjW4mk2X1zQMrbI

Freshman Kedon Slovis was making his second-career start after shredding No. 23 Stanford the week previous.

Zach Wilson led a 4th-quarter comeback to give BYU a 27-24 lead, but Slovis led the Trojans to a game-tying field goal to send the game into overtime.

After a Jake Oldroyd field goal, Slovis threw a pass over the middle that was deflected into the arms of Dayan Ghanwoloku, ending the game.
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2019 (14) Boise State 25 BYU 28
Line: Boise State -6.5
https://www.youtube.com/clip/Ugkx0mj3_Xp1BIktPu7NqXNYylzPCez0gWFC

Boise State came into the game undefeated, whereas BYU was had just lost to South Florida, Toledo, and Washington. Zach Wilson and Jaren Hall were both out with injuries, forcing freshman quarterback Baylor Romney into his first start.

A series of trick-play touchdowns to Matt Bushman gave the Cougars a commanding 28-10 lead that the Broncos whittled down to 3 late in the 4th quarter.

Facing a 4th & inches at their own 34 with 2:17 remaining, Austin Kafentzis snuck the ball up and over the 35 for a first down, ending the game.
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2019 BYU 42 Utah State 14
Line: Utah State -3
https://www.youtube.com/clip/Ugkxs2GypiSokUWzkbrefyoVVpsfk9o80tUY

It was uncertain whether Baylor Romney or Jaren Hall would start this game. Jaren was three weeks removed from a concussion and, although Romney had finished the game against the Broncos, he had an injured ankle that made it hard for him to move around.

It turned out that it didn't matter who the quarterback was. Hall led the Cougars to a 21-14 halftime lead, but surprisingly did not return the second half. Romney picked up where Hall left off and led the Cougs up and down the field on the Aggies despite a bum leg.
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2021 (21) Utah 17 BYU 26
Line: Utah -7
https://www.youtube.com/clip/UgkxvFFj2_EyX2M_3TnLj0NiDI7obxV3r9Nf

BYU had its work cut out against, arguably, one of the greatest teams in college football history. A team that would go on to don rose-themed helmets and earn itself a prestigious Rose Bowl loss. How could the Cougars possibly hope to compete against this future Rose Bowl loser? Rose Bowl.

It actually was fairly easy. BYU's front seven bullied the Ute offensive line all game long. BYU's offense played clean and delivered in clutch moments.

The only asterisk to this win was the soon-to-be Rose Bowl runner-ups weren't yet led by Cam Rising, the greatest non-big game quarterback in college football history, who apparently couldn't beat out Charlie Brewer in practice.

Did I mention this team went to the Rose Bowl?
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2021 (19) Arizona State 17 (23) BYU 27
Line: Arizona State -3
https://www.youtube.com/clip/Ugkx4wWObQhvFTTdiyAbV_zSiCdXcwVFdq0b

If the greatest football team of all time wasn't able to beat BYU at home, did people really think Arizona State would be able to do it the following week?

Maybe people thought BYU wouldn't be able to follow an emotional win over the Utes with another win over a ranked Pac-12 opponent. The game was tough, but a timely Tyler Allgeier punch and some help from the ROC got the job done.
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2022 BYU 31 Boise State 28
Line: Boise State -9.5
https://www.youtube.com/clip/Ugkx-jQBU-yypU4-TP6tO4vCeJe-5QKQsuXR

At this point in the season, BYU's offense was still capable of thriving. But that didn't seem to matter given the defense gave no resistance in the previous three games.

Then there was the black magic of the blue turf working to rob BYU of every opportunity to take control of a game they clearly were dominating (it would not have been the first time).

But Puka Nacua refused to not come down with a 4th & Goal fade pass, and the Cougar defense held on for the win.
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2022 SMU 23 BYU 24
Line: SMU -4.5
https://www.youtube.com/clip/UgkxktJsJMiClEL2BZYN5E0aNtPFwk-dfKmj

SMU had put up 77 points in a game against Houston. BYU had *that* defense. Then factor in the absence of Jaren Hall (injury), backup Jacob Conover (transfer), second backup Cade Finnagan (injury), and Puka Nacua (injury). In total, there just didn't seem to be any scenario where BYU puts up enough points to win.

But Sol-Jay and the BYU defense stepped up and did just enough to do exactly that.
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BONUS

Wins you may have thought were upsets but weren't (according to the game spreads I found):

2011 BYU 14 Ole Miss 13
Line: BYU -2

2020 BYU 55 Navy 3
Line: BYU -1

2022 Baylor 20 BYU 26 (2OT)
Line: BYU -2.5