Chase Budinger added 18 points and 12 rebounds as the Wildcats (19-9, 10-7) won their second straight despite falling out of the race for the Pac-10 title.
Arizona, which must win Saturday at Stanford to avoid finishing with its fewest conference victories in 22 years, still has ample reason to hope for a top-four seed at next week's Pac-10 tournament and an at-large bid to the NCAA tournament.
Ayinde Ubaka scored 15 points and Omar Wilkes had 10 for the Golden Bears (14-15, 6-11), who lost their third straight despite holding the Pac-10's highest-scoring club well under its 79.6-point average.
Arizona took control of a tight game with an 11-2 run late in the second half, including five straight points by Williams while the Wildcats mostly shut down Cal.
The Bears weren't helped by coach Ben Braun, who got a technical foul with slightly more than 5 minutes left for stomping onto the court to protest a no-call. Radenovic, who also had eight rebounds, hit one free throw to put Arizona up 65-59, but neither team scored again until Anderson converted a three-point play with 1:03 left.
Jawann McClellan then hit one free throw for Arizona, but Ubaka hit a 3-pointer with 30 seconds left to trim the Wildcats' lead to 66-65. Williams then hit two more free throws and Ubaka missed a straightaway 3-pointer, leading to two final free throws by Mustafa Shakur, who went 1-for-9 from the field.
Earlier, the teams even played through the earthquake that struck the Bay Area with 17:35 left in the second half. The Haas Pavilion crowd issued a collective "Oooh" as the building shook, then cheered as officials briefly delayed the game.
The clubs traded the lead in the first half before Shakur threw in a blind layup while sprawling to the floor at the halftime buzzer, putting Arizona ahead 36-34.