The Utes' defense forced a pair of turnovers in the third quarter to quiet No. 5 Stanford. The Cardinal only gained 48 yards in the third quarter.
Utah quarterback Travis Wilson completed 21 of his 29 attempts for 220 yards and two scores through three quarters.
Bubba Poole led the Utes with 111 yards rushing and added 68 yards receiving.
Dres Anderson ran for a score and caught a score to help Utah build a 21-14 lead over Stanford at halftime at Rice-Eccles Stadium.
Utah evened the score in the first quarter on a 4-yard swing pass to Williams, but Stanford responded by returning the kickoff 100 yards to regain the lead.
But Wilson hit Anderson with a 51-yard pass to even the score just before the end of the first quarter.
The Utes forced the Cardinal to punt three times in the second quarter. Stanford only gained 69 yards in the second quarter.
Utah's drive to take the lead in the second quarter took 11 plays and covered 99 yards.