Betts went deep to left off Beau Brieske (0-1), scoring pinch-hitter Will Smith and Shohei Ohtani.
Betts hit a two-out solo shot that put the Dodgers ahead 3-2 in the eighth before Detroit tied it in the ninth on Manuel Margot’s RBI single.
Dillon Dingler homered and tripled in the 10th to give Detroit a 5-3 lead in the top of the 10th.
Tied at 3, left fielder Michael Conforto came up short trying to catch the ball hit by Dingler, allowing Riley Greene, who began the inning at second, and Zach McKinstry, who was intentionally walked by Luis Garcia (1-0), to score.
The Dodgers got a run back in the bottom of the 10th to trail 5-4 on Conforto's ground-rule double before Betts' heroics.
Dingler homered in the second off Yoshinobu Yamamoto to give Detroit a 1-0 lead.
The Dodgers tied the game at 2 on Freddie Freeman's two-run homer off Detroit starter Jack Flaherty.
The Dodgers began the night walking a blue carpet to an infield stage where they received blue boxes containing glittering rings to mark their World Series win over the New York Yankees last year.
The crowd of 52,029 gave Flaherty a standing ovation when he left in the sixth, their thank you to the Burbank, California, native who started Game 1 of the National League Championship Series and Game 1 of the World Series, both at Dodger Stadium.
Flaherty will get his World Series ring before Saturday’s series finale.
Key moment
A safe call at home in the ninth was overturned, denying the Tigers a chance to take the lead after Margot was thrown out at the plate.
Key stat
Dodgers starter Yoshinobu Yamamoto had a career-high 10 strikeouts.
Up next
RH Reese Olson makes his season debut for the Tigers on Saturday. RH Roki Sasaki (0-0, 3.00 ERA) starts for the first time at Dodger Stadium in the series finale.
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AP MLB: https://apnews.com/hub/mlb
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