Rihards Kuksiks had 17 points and Jeff Pendergraph finished with 16 points and 12 rebounds for the Sun Devils (21-5, 10-4 Pac-10), who won their fifth straight game.
Nic Wise had 17 points and seven assists, while Kyle Fogg and Jordan Hill each scored 14 for the Wildcats (18-9, 8-6), who lost for the first time in their last eight games.
Arizona State began the second half with a 44-34 advantage, and led by 11 at one point when Jamelle Horne's jumper touched off a 13-0 Wildcats' run that put Arizona ahead 62-60 with 4:14 left to play. Kuksiks hit a 3-pointer with 1:16 to go that put State in front 68-66, but Hill tied it at 68-68 with a layup at 19:05.
Pendergraph sank two free throws with 25.6 seconds left to make it 70-68 Sun Devils. Arizona had a chance to tie the game in the closing seconds but Hill and missed a layup and Derek Glasser missed the front end of a one-and-one just before time expired.