Rudy Carpenter completed 16-of-31 passes for 200 yards and a touchdown for the Sun Devils (9-1, 6-1 Pac 10), who still have a chance for a slot in the BCS bowl.
Keegan Herring rushed for 116 yards -- 71 yards for a touchdown -- while Chris McGaha had nine catches for 123 yards for Arizona State, which will play host to 15th-ranked USC next Saturday.
Rasshan -- listed fourth on the UCLA quarterback depth chart -- was 14-of-27 for 181 yards with one interception, and also added 41 yards on 13 carries for UCLA (5-5, 4-3 PAC 10), which lost for the fourth time in its last five games.
Matthew Slater returned a kickoff 89 yards for a UCLA touchdown.
Arizona State trailed, 13-10, at halftime but quickly scored two third-quarter touchdowns to take a 24-13 lead.