UCLA trailed by 12 midway through the second period but came back thanks 20 points from Drew and 16 from Shabazz Muhammad.
The Bruins (24-8), the top seed in the tournament, will face Arizona in Friday's semifinals after the Wildcats got past Colorado 79-69.
Drew gave UCLA a 67-66 lead at the 5-minute mark and the Bruins moved in front for good on back-to-back jumpers from David Ware in the final 2 minutes.
Jordan Bachynski led Arizona State with 22 points.
Arizona stormed to a first-half lead and held on against Colorado to reach 25-6 for the season. Nick Johnson scored 18 points to lead the Wildcats, who have lost both their meetings with UCLA this season by a combined 16 points.
Utah opened the evening session Thursday with a surprising 79-69 overtime decision over second-seeded California.
The Utes dominated the extra period after jarred DuBois hit a 3-pointer with 9 seconds left in the second half to tie it. California then managed only two points during the first 4 minutes of the overtime.
Utah will take a 15-17 record into its semifinal meeting against either Washington or Oregon.
Celebrity Couples of 2014 [PHOTOS]