Lowe won it with his 18th homer off Kenley Jansen (3-6), who had his streak of converting 20 consecutive chances end. Erasmo Ramirez (3-3) got the win.
“Every walk-off is going to feel nice,” Lowe said. “Every walk-off homer is going to feel better.”
Luis Urías hit an RBI single in the 11th inning to give Boston a 6-5 lead, a flare to shallow right that went of the glove of Lowe at second base.
“It’s September,” Lowe said. “Any win that we can grab at this moment we’re going to take it. We understand we need to be better in every facet, so understand it, take it in."
The Rays loaded the bases in the 10th with one out against John Schreiber but failed to score when Josh Lowe was thrown out by right fielder Adam Duvall trying to score from third on Christian Bethancourt's fly.
Boston started the day 4 1/2 games out of the final AL wild-card spot. The Rays hold the top AL wild-card spot.
“It is what it is. We just have to keep playing hard, keep going,” Boston manager Alex Cora said.
Tampa Bay's Zach Eflin failed to become the AL's first 14-game winner despite departing with a two-run lead. He gave up three runs and five hits over five-plus innings.
Justin Turner had an RBI infield single in the sixth and drove in another run on a base-hit in a two-run seventh as Boston rallied to tie it at 5. Triston Casas got Boston even and extended his career-high hitting streak to 12 games with his 177-foot pop-up single down the left-field line.
Turner set a career-high with 91 RBIs.
René Pinto hit a two-run homer off Kutter Crawford during a three-run second as the Rays took a 3-0 lead. The Rays went ahead 5-2 in the fourth.
Crawford allowed five runs, three hits and four walks over 3 2/3 innings in a season-high 96-pitch outing. The right-hander was coming off a loss against the Houston Astros last Wednesday in which he gave up six runs in 2 2/3 innings.
Boston loaded the bases with no outs after Turner's sixth-inning run-scoring hit but failed to score again.
“We didn’t cash in there,” Cora said. “We had the lead at one point. Just one of those (games). It’s tough, but we’re going to show up tomorrow.”
Enmanuel Valdez cut the Red Sox deficit to 3-2 on a third-inning two-run homer. Ceddanne Rafaela had three hits for the Red Sox.
The announced crowd was 9,119. Tampa Bay entered averaging 18,067, which is the fourth lowest in MLB.
Red Sox: OF Alex Verdugo (left hamstring) missed his second straight game and will likely sit out Wednesday. … RHP Corey Kluber (right shoulder) threw 32 pitches over two innings of live BP and will pitch in a minor league game Friday night.
Rays: SS Taylor Walls (groin) sat out for the second consecutive game but could be back in a couple days.
Rays RHP Tyler Glasnow (7-5) will start Wednesday night’s game. RHP Nick Pivetta (9-7) will start for Boston.
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