Falk's three touchdown passes pushed him past Matt Barkley as the Pac-12 leader in career touchdown passes. The senior has thrown 118 TD passes. Barkley totaled 116 at USC.
Washington State (9-2, 6-2 Pac-12) earned its third straight win in the series with the Utes (5-5, 2-5).
Tyler Huntley threw for 293 yards and a touchdown and added 51 yards on the ground to lead the Utes. Huntley also threw four interceptions, part of seven Utah turnovers overall. The Cougars scored 23 points off those turnovers.
Washington State capitalized on early Utah turnovers to jump out to a 13-0 first-quarter lead. The Utes had two fumbles and an interception over three straight drives to give the Cougars short fields.
Robert Taylor stripped the ball from Demari Simpkins after a first-down catch on Utah's second drive of the game, with Jalen Thompson recovering at the Utah 46. Falk converted three third downs on the drive, including a 11-yard screen pass to Tavares Martin Jr. for a touchdown.
Taylor intercepted Huntley near midfield on Utah's third drive to set up a 44-yard field goal from Erik Powell. Then, on the Utes' fourth drive, Hercules Mata'afa forced a fumble when he sacked Huntley and recovered the ball on the Utah 19. Powell turned that turnover into a 32-yard field goal.
Utah settled down and rallied in the second quarter.
A 56-yard field goal from Matt Gay put the Utes on the board. Then Zack Moss punched it in from 2 yards out to cut Washington State's lead to 13-10. Demari Simpkins set up the score when he hauled in a 71-yard catch down the middle of the field to get Utah inside the 10-yard line.
Falk helped steal back some momentum when he tossed a 1-yard pass to Kyle Sweet to put the Cougars up 20-10 with 3:02 left in the second quarter.
Utah cut it to 26-18 in the fourth quarter on a 1-yard dash from Moss. Then Thompson recovered another fumble at the Utah 14, setting up a 6-yard strike from Falk to Isaiah Johnson-Mack. It gave Washington State a 33-18 lead with 8:23 left, dimming comeback hopes for the Utes.
Utah narrowed the gap again on a 12-yard touchdown catch by Raelon Singleton. The Utes were driving again for a possible tying touchdown when Chima Onyeukwu snagged a tipped pass at midfield with 58 seconds left to secure the win.
NOTES: Utah K Matt Gay has made five field goals of 50 yards or longer this season, the most of any kicker in the nation. His 56-yarder in the second quarter matched a career-high set against San Jose State on Sept. 16. ... Washington State DT Hercules Mata'afa had three sacks, four tackles for loss and a forced fumble in the first half. ... Utah had two yards on 29 carries in the first three quarters. ... Washington State totaled seven sacks and 11 tackles for loss. Utah lost 60 total yards on those plays.