Ahead by only six at halftime, the Cardinal (3-0, 1-0 Pac-12) outscored Arizona 21-0 the rest of the way, with Luck hitting Zach Ertz on a 16-yard scoring strike in the third quarter and Levine Tollolo on a 34-yarder in the fourth.
Luck finished 20-of-31 for 325 yards and no interceptions. Stepfan Taylor piled up 153 yards rushing on 22 carries for Stanford.
Nick Foles completed 24-of-33 through the air for 239 yards, one TD and no interceptions as the Wildcats (1-2, 0-1) lost their second straight game.
Keola Antolin carried the ball nine time for 63 yards for Arizona.