Davonte Lacy of Washington State (11-8, 3-4) hit a 3-pointer, was fouled and missed the ensuing free throw to give the Cougars a 77-74 lead with 18.3 seconds remaining.
"I think the score was 62-62 at one point and I missed a big (3-pointer)," Lacy said. "I said to myself I was not going to be scared to shoot it (again), I did and it went in."
With six seconds left, Justin Cobbs of California (16-5, 6-2) hit the front end of a pair of free throws, but missed the second. Jorge Gutierrez grabbed the rebound and flung a shot that hit the front of the rim to seal the Cougars' victory.
"(California) is a very good, very physical team," WSU coach Ken Bone said.
California led for most of the game, including a 40-34 advantage at halftime. The deficit would have had much larger had it not been for Aden's heroics as he came off the bench to score 16 of his 24 points in the game's first 20 minutes.
"Aden had a great weekend. Most coaches would start him," Bone said with a laugh. "(But it's) how you fit into the whole system, not just who scores the most points. He did a lot of nice things for us."
WSU took its first lead when Abe Lodwick hit a 3-pointer with 16:28 left in the game, but the Bears responded with a 9-0 run for a 53-47 lead.
Cal hung onto that lead for the majority of the second half, but was never able to take more than a seven-point advantage.
With 6:51 left in the game, Aden, who scored 33 points on Thursday against Stanford, hit a pair of free throws to tie the game at 62.
The Golden Bears led until Brock Motum hit from the paint with 1:32 left to tie the game at 74-all.
"I liked the way we competed," Bone said. "When you compete hard, scrapping, it's not always pretty, but at the end of the day I think you give yourself a chance to win."
Motum, who finished with 15 points, said he's excited about the way the Cougars fought against a powerful California team.
"Tonight was another step forward," he said. "(California) is a really good team. They put up a fight all night long. It's a good confidence booster to beat (California) and Stanford this weekend."
WSU had four players finish in double figures and California had five players accomplish the same.
The Golden Bears outscored WSU 22-5 off turnovers.