Maynard continued his late-season surge by completing 19-of-26 passes for 237 yards and one touchdown, which the transfer from Buffalo floated over the head of a defender to running back C.J. Anderson, who scampered 74 yards for the score.
Anderson also had two rushing touchdowns, while Maynard added 40 yards and a touchdown on the ground.
Giorgio Tavecchio made all four of his field goals, connecting from 48, 27, 19 and 30 yards. The senior has now made 19 of his 22 tries this season.
The Cal (7-5, 4-5 Pac-12) defense limited Arizona State (6-6, 4-5 Pac-12) to 10 points after intermission and also forced four takeaways, twice intercepting quarterback Brock Osweiler.
The Sun Devils lost any chance of playing in the inaugural Pac-12 championship game after Colorado upset Utah, 17-14, earlier Friday. With wide swaths of empty seats visible to the national television audience, the loss likely marks the end of Dennis Erickson's disappointing tenure in Tempe.