Favors' three-point play tied the game near the end of regulation. Then the 6-foot-10 post scored the first two baskets of overtime to spark a 6-0 Utah run.
"He's been waiting for the opportunity," Utah guard Devin Harris said. "He's been poised and playing well. The last game he really stepped it up defensively, blocking shots.
"He got a lot more opportunities tonight and took advantage."
Favors fought the natural tendency of a young player to rush things early. Although he and the Jazz began with fits and starts, eventually, Favors found his rhythm.
By the fourth period, Favors as well as Utah's other young players, Gordon Hayward, Alec Bucks, Jeremy Evans and Enes Kanter, provided solid minutes.
The group combined for 53 points and 46 rebounds. Overall, Utah owned the glass, outrebounding Golden State (18-24) by 25, including 20 offensive rebounds.
Kanter also grabbed a career-high 13 rebounds.
"Everybody had to step up … including myself," Favors said. "We're trying to get back into the playoff race. We've got to start playing like a playoff team. I think we showed that tonight.
"I've got to come out every night and be ready to play, whether it's scoring, defense, rebounding, whatever. I have to be ready."
Favors, with career highs in scoring and rebounds, recorded his fourth double-double as the Jazz won their second consecutive overtime victory.
"Defensively, he did a great job coming up and being aggressive on the ball," Corbin said. "Offensively he was really patient and made the right moves. We really need that effort from him. He was relaxed and did a great job of just coming in ready to play and not forcing things early."