Betts and Mitch Moreland hit back-to-back homers for the go-ahead runs in the eighth inning and the struggling Red Sox beat the MLB-best Tampa Bay Rays 6-4.
"A lot of emotions going through my head there, but the main thing is it put us ahead," Betts said. "It's just one (game), but it's definitely a starting point. The main thing is I helped in some way today, and that's kind of my viewpoint on playing."
With the game tied at 4, Betts hit a leadoff shot off Diego Castillo (0-2) and Moreland connected three pitches later.
"You're talking about two pretty talented hitters," Rays manager Kevin Cash said. "Not surprising if you don't locate it or command it the way you want, they can make you pay."
Betts finished 2 for 4 and raised his batting average from .200 to 216. Last season, the Red Sox outfielder hit a big league-leading .346 with 32 homers and 80 RBIs on his way to the MVP award.
Christian Vazquez also homered and Brandon Workman (1-1) went 1 2/3 scoreless innings for the Red Sox, who are 7-13 and trail the AL East-leading Rays by seven games. Ryan Brasier worked the ninth to pick up his fourth save.
"The standings?" Boston manager Alex Cora said. "We know where we're at, but it's more about we've got two shots to win the series. That feels good."
The Rays are the last team in the majors to have consecutive losses this season. Castillo was also the loser in a 6-5, 11-inning loss to Baltimore on Thursday night.
"It's a long, long season," Cash said. "We'll be fine."
After 20 games last season, the eventual World Series champion Red Sox (17-3) were 10 games up on Tampa Bay (7-13).
Daniel Robertson, mired in an 0-for-21 slide, got the Rays even at 4-all with a two-run double during the sixth. The inning was setup when Boston third baseman Rafael Devers misplayed what looked a double-play grounder from Avisail Garcia with one on and no outs.
Devers had a run-scoring double in the fifth for Boston's first hit before Vazquez put Boston ahead 3-2 on his two-run shot to center.
Vazquez has three homers and eight RBIs in his last five games.
Betts, hitless in his previous 12 at-bats, doubled in the sixth and scored as the Red Sox grabbed a 4-2 lead when J.D. Martinez extended his hitting streak to nine games with an RBI single.
"I've been struggling all year, and to be able to hit a double in a spot like that, it definitely felt like a weight came off my shoulders," Betts said.
Martinez has a hit in 19 of 20 games this season.
Brandon Lowe hit his fifth homer in the last nine games, a solo drive that just cleared the fence at the 322-foot mark down the right-field line in the second before Garcia's third-inning RBI triple as the Rays went up 2-0.
Red Sox: 2B Dustin Pedroia was examined by doctors Thursday and it was determined that his latest left knee injury is not serious. "We're just going to let it calm down for a few days and then it should be all right," Pedroia said. He was hurt in Boston's game Wednesday night and went on the 10-day IL on Thursday.
Rays: Ace Blake Snell (fractured right fourth toe) will have a bullpen session Saturday. "He continues to heal really quickly, which we're very encouraged about," Cash. ... C Mike Zunino went on the paternity list.
Boston GM Dave Dombrowski and Cora presented Rays LHP Jalen Beeks with his 2018 World Series ring. Beeks appeared in two games last season with the Red Sox before being traded to Tampa Bay July 25 for RHP Nathan Eovaldi.
Red Sox RHP Rick Porcello (0-3, 11.12 ERA) and Rays RHP Charlie Morton (2-0, 2.18 ERA) are Saturday night's starters. Porcello is 8-5 with a 2.86 ERA in 15 road starts against Tampa Bay.
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