The Sun Devils (10-9, 2-4 Pac-12) scored 22 unanswered points and held the Golden Bears scoreless for more than 13 minutes in the first half to win their second consecutive win after opening conference with four straight losses.
Savon Goodman added nine points and seven rebounds for Arizona State.
The Sun Devils led by as much as 38 while extending their winning streak over the Bears to four. Barnes had 11 points in the second half while Justice added three 3-pointers.
Jordan Mathews had 11 points and five rebounds for California (11-8, 1-5). It's the second-worst loss in school history.