Westbrook also had 15 rebounds and seven assists. Paul George added 34 points and eight rebounds.
Utah takes a 3-2 lead back to Salt Lake City for Game 6 on Friday.
Oklahoma City took advantage after Utah's post players, Rudy Gobert and Derrick Favors, got into foul trouble. Both finished with five fouls, and Oklahoma City was able to get to the basket consistently for the first time in the series.
Utah opened the second half on an 8-1 run to go up 64-42, and Crowder's 3-pointer made it 71-46 with 8:34 left in the third quarter.
Westbrook hit back-to-back 3-pointers, then made a layup with 5:07 left in the third quarter to cut Utah's lead to 73-60. Gobert picked up his fifth foul with 3:46 left in the third quarter. Westbrook's 3-pointer tied the game at 78 heading into the fourth quarter. Westbrook scored 20 points in the third quarter.
Westbrook scored immediately at the start of the fourth to finally put the Thunder in front. Back-to-back threes by Westbrook and Alex Abrines put Oklahoma City up 96-91, and a jumper by Westbrook with 1:24 left put Oklahoma City up 107-99.
Tip-ins: Jazz: Shot 57 percent in the first quarter to take a 34-29 lead. Crowder scored 15 points in the first quarter. Mitchell was fouled on a 3-pointer with 11.1 seconds left in the first half. Before Mitchell shot his free throws, Thunder coach Billy Donovan was called for a technical. Mitchell made all four free throws, and Utah led 56-41 at the break.
Thunder: Former Thunder forward Enes Kanter, who was sent to New York in the deal that brought Anthony to Oklahoma City, attended the game. Kanter played for Utah before playing for the Thunder. George made a 3-pointer at the first-quarter buzzer.