Tyler Lamb totaled 10 points for the Bruins (11-9, 4-4 Pac-12), rounding out UCLA's list of double-figure scorers.
Chris Hines was the only Utah player in double figures with 13 points. The Utes (5-15, 2-6) have lost five of their last six and dropped to 0-4 on the road in Pac-12 play.
Ben Howland recorded his 200th career head coaching victory at UCLA, having logged a 200-92 record midway through ninth season as the Bruins' head coach.
"This was a good win for us," Howland said. "The guys came out and played very well defensively for 40 minutes. We did a good job sharing the ball and making good passes."
Anderson made 5-of-6 field goals, including 2-of-3 three-point attempts, and tallied three assists and three steals.
UCLA led 36-21 at halftime and outscored Utah by a 26-12 margin in the opening 10:29 of the second half to secure a 62-33 cushion.
Leading 30-21, the Bruins received a pair of free throws from David Wear with 1:50 to play before halftime to secure an 11-point cushion. UCLA never trailed by fewer than 11 points for the remainder of the game.
"We had a 15-point lead at halftime, so in the locker room I told them to build on that in the second half, especially in the first five minutes. Our senior guards played very well tonight. Jerime Anderson had one of his best games as a Bruin. He really controlled things out there."
The win helped UCLA even its Pac-12 record to 4-4.
The Bruins return to action against Colorado (14-6, 6-2) on Saturday at the Los Angeles Sports Arena. Game time is 1 p.m. The contest will be televised live on Prime Ticket.