Johnson also had seven rebounds for Arizona (26-2, 13-2 Pac-12), and Kaleb Tarczewski scored 16 points.
Aaron Gordon and T.J. McConnell both had 13 points for the Wildcats.
Justin Cobbs led Cal (18-10, 9-6) with 12 points. Richard Solomon and Tyrone Wallace both had nine.
Cal started quickly with an 8-2 run to start the game; however Arizona went on a 9-0 run late in the half to take the lead for good. Arizona led 44-29 at halftime and did not allow the Golden Bears to get closer than nine points in the second half.