Cal won the first meeting 60-58 on a last-second jumper by Justin Cobbs that sent the students pouring onto the court.
Arizona (26-2, 13-2 Pac-12) ran away from the Bears early in the rematch, using a big first-half run and good shooting (50 percent) all game to prevent the season sweep.
T.J. McConnell had 13 points and six assists, and Rondae Hollis-Jefferson provided a lift off the bench with 12 points and 10 rebounds. Johnson also had seven rebounds and five assists after struggling the first game against the Bears.
Cal (18-10, 9-6), struggled at times against Arizona's defensive pressure and had little chance of stopping the Wildcats at the other end to lose for the 17th time in 19 games at McKale Center.
Cobbs led the Bears with 12 points.
Arizona wanted a little revenge after what happened in the first meeting against Cal.
The Wildcats entered the Feb. 1 game with the No. 1 ranking and a school-record 21-game winning streak. They left Berkeley with their first loss of the season — thanks to Cobbs' stepback jumper with 0.9 seconds left — and with forward Brandon Ashley in a walking boot after he injured his right foot going up for a rebound in the first half.
Ashley is done for the season, but Arizona has found ways to win without him, picking up three victories in four games, including Sunday's 88-61 blowout at Colorado.
The Wildcats started slowly in the rematch against Cal, opening 1 for 6 to miss more shots in the first 3 1-2 minutes than they did the entire half against Colorado (22 for 26).
Once they got rolling, the Bears couldn't keep up.
Triggered by its defense, Arizona went on a 12-2 run, building its lead to 39-23 on a series of steals and dunks.
Johnson had one dunk in transition after a steal and Aaron Gordon had another, racing off for a head-above-the-rim reverse dunk that triggered a roar inside McKale Center.
Hollis-Jefferson had a high-flying dunk on an alley-oop pass on an inbounds play, then threw down a tomahawk in transition after Johnson tracked down Cobbs to block his layup from behind at the other end.
Arizona made 18 of 36 shots to lead 44-29 at halftime. Johnson had 12 points on 5-of-8 shooting, four rebounds and three assists after scoring four points on 1-of-14 shooting the first game against Cal.
The Wildcats quickly built the lead to 20 points in the second half, but Cal showed a little resiliency, going on an 11-0 run that cut Arizona's lead to 53-44.
That was as close as the Bears would get.
Arizona turned up the pressure again, McConnell hit a 3-pointer in transition and Gordon soared in for another dunk, putting the Wildcats back comfortably ahead, 70-52.