Note that this is not based on name brand of teams, otherwise victories over Texas, USC, Tennessee etc teams would be higher, even when those teams were bad.  This is based on the most impressive on-field results based on opponent quality

1. 2021 #21 Utah: Only #21 at the time, but Utah finished #12 in the AP Poll and #11 Sagarin, making this the best EOS victory for BYU in the independence era and the only victory over a P5 that finished the season ranked.
2. 2018 #6 Wisconsin: The highest rated (as of gametime) victory, though Wisconsin would go on to have a somewhat disappointing season, finishing 8-5 and unranked in the poll (though Sagarin did have them #25, so they were still a pretty good team)
3. 2022 #9 Baylor: this one was amazing at the time...but suffers a bit in retrospect since Baylor ended up with a losing record (albeit a respectable #27 in end of season Sagarin)
4. 2012 Utah St: Unranked at the time, but finished #16 in the AP poll and #19 by Sagarin. Honestly, this one has a real argument to be #2...but I just couldn't do it.
5. 2019 #14 Boise St: One of the only 2 times (along with #1 on this list) that we beat a team that was both ranked at the time (#14) and at the end of the season (#23) though Sagarin has them down at #32
6. 2013 #15 Texas: Huge at the time, but finished 8-5 and unranked (#30 by Sagarin). Still good, but a bit less than it could have been
7. 2019 #24 USC: Finished 8-5 and unranked, but at least they were close (#26 Sagarin).  Texas' higher (at-the-time) ranking is enough to push that one ahead, but very similar.
8. 2021 #19 Arizona St: This is the budget version of the 2022 Baylor victory, not quite as good as it seemed at the time, with Arizona St finishing #36 in end of season Sagarin, but 8-5 at least
9. 2015 #20 Boise St: The lone ranked victory in 2015. Ultimately Boise St did not have an impressive season though, finishing unranked and #38 by Sagarin 
10. 2020 #21 Boise St: The lone ranked victory in 2020. Ultimately Boise St did not have an impressive season though, finishing unranked and #41 by Sagarin
11. 2021 Utah St: Not a huge deal at the time...but one of only 4 times (along with #1, #4, and #5) that BYU beat a team that finished the season AP Ranked, with USU ending up #24.  Only #55 by Sagarin though and not ranked at the time, so other games rank ahead, but that final AP rank keeps this one from falling too far.  Without it...this game probably comes in in the 20s
12. 2019 Tennessee: Not ranked at the time, not ranked later, but still a good SEC team and #35 by Sagarin. The lack of the opponent ever being ranked holds this one down some, but it's the best of that group
13. 2011 Tulsa: A game nobody would expect to have near the top 10... but Tulsa finished 8-5 with a surprisingly high #35 Sagarin ranking. 2019 Tennessee also going 8-5, but against better competition, gives them the edge for the #12 spot  
14. 2020 UCF: Rates as the best EOS victory in a magical 2020 season, with UCF coming in as the #37 team by Sagarin
15. 2013 Utah St: 9-3 and the MWC Champion with a #41 Sagarin ranking
16. 2013 Georgia Tech: Finished just ahead of Utah St by Sagarin ranking (#37), but the disparity in records (GaTech went 7-6) and USU being the MWC champs is enough to put USU just ahead
17. 2015 Nebraska: Nebraska finished 6-7 and #42 by Sagarin, so they weren't really a very good team...but they also weren't a bad team. Even ignoring their name/brand, this was one of the better wins of the Independence Era.
18. 2021 Washington St: Could easily be flipped with Nebraska above.  Wazzu finished 7-6, but #45 by Sagarin
19. 2012 Georgia Tech: Another toss-up, very similar.  Finished 7-7 but #46 by Sagarin. 
20. 2016 Mississippi St: Continuing the trend, this team was actually pretty mediocre, despite the name. Not as bad as 2021 USC, 2016 Michigan St or 2011 Ole Miss though so they still make the list, despite being 6-7 and #47 by Sagarin.  Really, these previous 4 are all interchangeable.
21. 2022 Boise St: Finished an impressive 10-4 and #52 by Sagarin
22. 2016 Toledo: A suprising entry here, but they were #52 in Sagain that season and finished 9-4.  An underappreciated solid victory
23. 2013 Houston: 8-5 with a #50 Sagarin rank.  Not anything incredible, but gets them onto the list
24. 2014 Virginia: Rinse and repeat.  Another P5 opponent with a poor record (5-7) and middling Sagarin rank (#51)
25. 2014 Texas: Finished 6-7 and #53 by Sagarin, right behind UVA (above) and Utah St (who was #52 and beat us that year).  Not a good team or as big a victory as the name indicates... but still manages to sneak into the Top 25

Next 5 Out

• 2020 San Diego St: Only 4-4, but #59 by Sagarin means that they barely miss the cut here, ekeing out 2014 Cal by virtue of not having a losing record
• 2014 Cal: 5-7 with a #59 Sagarin rank sneaks them onto the very end of this list over several very similar opponents
• 2021 Virginia: 6-6 and #64 Sagarin.  Not terrible, but not quite enough to make the list
• 2018 Arizona: 5-7 and #65 by Sagarin. Not a gimme win... but also not impressive enough to come into the Top 25
• 2012 San Diego St: 9-4 and #66 by Sagarin

Notable Omissions

• 2021 USC: People will wonder where this game is...but USC finished 4-8, #73 by Sagarin and fired their head coach. This game shouldn't even get HM and is only here because people will ask about it. Note that the 2019 victory is #7 though.
• 2016 Michigan St: Another big name; another terrible team. They finished 3-9 and #84 by Sagarin
• 2011 Ole Miss: Incredibly meaningful (from a tone/symbolism standpoint) as the first game of Independence and a win against an SEC team..but they were terrible. 2-10 and #103 by Sagarin

So let's hear it.  What games am I missing?  I'm sure there's at least one that should be in there that slipped my mind