The 10th-seeded Utes trailed 59-56 in regulation after Allen Crabbe hit two free throws, but Utah worked the ball around to DuBois, who hit a contested 3-pointer with 4 seconds left to tie the game. Utah dominated overtime and will move on to face the Washington-Oregon winner in Friday's semifinals.
Cal (20-11) needed to play well in the Pac-12 tournament to ensure an NCAA invite but now will have to wait three anxious days to find out if it will get an at-large bid.
Justin Cobbs had 26 points and Crabbe finished with 21 for the Bears.
Jason Washburn had 18 points for Utah.
"It's unbelievable," said Utes head coach Larry Krystkowiak. "We had an opportunity to fold the tent at one point. We got down, and our kids defended their butts off. We missed a bunch of open shots and I just told them to hang in there. All of a sudden the rim opened up and it was a fantastic evening."
"We read an excerpt from a book and it had one word, and that was 'believe,'" said DuBois. "Regardless of our record, we knew if we believed we knew we can do anything. That's what showed tonight."
Utah needs to win the Pac-12 tournament to get into the NCAA tournament and took the first step by holding off USC 69-66 in its tourney opener. It was a good step for the Utes, a young team that struggled to close out tight games, even against smaller opponents like Sacramento State and CS Northridge.
To keep it going, they would have to beat Cal, one of the hottest teams coming into the Pac-12 tournament.
The Bears had some rough patches during the nonconference schedule -- three straight losses against ranked opponents in December -- and opened Pac-12 play with a mediocre 5-5 start.
Cal gathered some confidence by sweeping the Oregon schools -- the Ducks were ranked No. 23 at the time -- and closed conference with nine wins in 11 games. The Bears stumbled in the season finale with a 13-point loss to rival Stanford but still earned the second seed in the conference tournament and a coveted first-round bye.
Cal won the first meeting with Utah by five, then dominated the Utes after getting off to a slow start, using a 21-0 run to win 64-46.
Utah shot 29 percent in the blowout loss but dialed in on the rim Thursday night, hitting 10 of its first 14 shots.
DuBois scored 15 of his 22 points in the second half against USC and was still hot in the first half against Cal, scoring 15 points on 6-of-7 shooting.
Cobbs was right there with him, scoring 13 points on 5-of-7 shooting to give Cal a 33-32 halftime lead.
The second half started off a bit more defensive-oriented. Make that a lot more -- the teams traded air balls and passes that sailed off the backboard.
Utah missed 10 of its first 12 shots and went nearly 7 minutes without a field goal until Brandon Taylor scored on a three-point play.
Cal was only a little better, allowing the Utes to stay close despite their clanging.
Utah will play Oregon in the semifinals Friday night at 9:30 p.m. mountain time.