The Bruins fought back from a 10-point, second-half deficit, but the win was tempered by the loss of Jordan Adams in the game's final seconds.
Adams, who scored 24 points to lead UCLA, suffered a broken right foot that is expected to keep him out of post-season play.
UCLA will meet Oregon in the championship match on Saturday after the Ducks coasted past Utah 64-45.
It was a missed 3-point attempt by Adams that led to Anderson's rebound and layup for the winning points. The Bruins then survived a missed jumper by Solomon Hill and another miss by Grant Jarrett after he had grabbed the offensive rebound.
UCLA improved to 25-8 and will try to add the conference tournament title to the regular-season crown they won this year.
No. 18 Arizona dropped to 25-8.
Oregon limited Utah to 15 first-half points and coasted to a win that set up a third and deciding game against the Bruins this season. The Ducks and Bruins each won on their own court during the regular season.
Damyean Dotson and E.J. Singler both scored 14 points in the defensive battle to lead Oregon (25-8). Utah shot just 33 percent from the field.