The Buckeyes (21-13) advance to play host to a quarterfinal game on Wednesday night against Dayton.
Kosta Koufos had 17 points, and Othello Hunter controlled the paint with one of the best games of his career, grabbing a career-high 16 rebounds to go with 11 points.
Jerome Randle had 18 points, and Ryan Anderson, averaging 21.4 a game, added 11 for Cal.
The Buckeyes had a run in which they outscored the Golden Bears 24-4 to take command.
DAYTON 55, ILLINOIS STATE 48
In Normal, Ill., Dayton went on a 17-0, second-half run to break open a close game en route to a victory over Illinois State in the second round.
Dayton (23-10) was led by Brian Roberts with 16 points.
The Flyers trailed by four with 17:03 left before Illinois State (25-10) went more than 10 minutes without scoring. The Redbirds missed 12 shots in a row.