Yes, Utah upset BYU several times in the 1990's, including a couple times when BYU was already the conference champion or bowl bound and the rivalry game was all Utah was playing for.

But even with a bizarre 3 game skid from 93-95 (bizarre, because BYU was a Top 25 program with 20+ years of rivalry dominance and Utah was working it's way out of the cellar and playing in a crumbling wooden matchbox of a stadium), BYU had the better of the rivalry from the early 1990's to the early 2000's, with wins in 1990, 1991, 1992, 1996, 1998, 2000, and 2001.

From 2002 to present BYU has won 3 times: 2006, 2007, 2009. 16 games, 3 wins.

9 more games with 4 wins (which would be the 1993-2018 period) shows that percentage wise, the 2002-2018 period is where Utah has dominated.