Arizona State led by as many as 15 in the second half and 12 going into the final 10 minutes but UCLA clawed back to escape with the win.
UCLA (23-8) next meets the winner of a game later Thursday between No. 18 Arizona and Colorado. Arizona State (21-11) was eliminated from the tournament.
The Sun Devils used 14 first-half points from Jordan Bachynski in enjoying a lead through the opening period. It was another Bachynski basket that put Arizona State ahead 53-38 with 16:43 to go.
Shabazz Muhammad scored six straight points for UCLA that got the Bruins within 66-64 and Larry Drew II hit a three-point shot with 4:59 to go for the first UCLA lead since it was 7-5.
Evan Gordon and Wear traded a pair of free throws each that kept the score tied at 74-74. Gordon made another free throw but Wear hit back-to-back jumpers, the second with 11 seconds to play, and UCLA was up 78-75.
Drew scored 20 points to lead the Bruins and Muhammad had 16. Wear's late barrage allowed him to total 15 points.
Bachynski paced the Sun Devils with 22 points while Jahii Carson added 21and Jonathan Gilling 17. The rest of the team managed 15 points.
N.J. man wakes up from 10-hour sleep with knife in back
Exploding whale video goes viral on Internet