Wilson made good on 23-of-34 attempts and Bubba Poole provided 186 yards of total offense for the Utes (4-2, 1-2 Pac-12), who rebounded from a loss to UCLA last week.
Poole rambled for 111 yards on 22 carries while also catching seven passes for 75 yards.
The Cardinal (5-1, 3-1) had its 13-game winning streak snapped as Kevin Hogan was held to 246 yards and a touchdown on 15-of-27 efficiency.
Tyler Gaffney led Stanford's ground game with 108 rushing yards and a score on 16 carries.
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