In the newest rankings out Sunday, Arizona State moved up to No.6 while California fell out of the top 25.
The Sun Devils (8-0, 5-0 Pac-10) trailed, 20-14, at the start of the third quarter, but scored the game's final 17 points to beat a ranked opponent for the first time this season.
Nance, who scored twice in the second quarter, rushed for 85 yards on 21 carries.
Cal's Nate Longshore went 18-for-36 for 261 yards, with one touchdown and two interceptions.
Wide receiver DeSean Jackson scored once on five catches for 88 yards, and Justin Forsett rushed for 62 yards on 17 carries for the Golden Bears (5-3, 2-3), who have dropped three in a row after opening the season with five straight wins.
Swim Week Miami Beach 2014 [PHOTOS]