BOSTON -- Matt Moore left the Tampa Bay Rays wanting more Tuesday night.

The Rays left-hander bounced back from a 32-pitch first inning to log 6 2/3 quality innings, leading Tampa Bay to a 5-2 victory over the Boston Red Sox in the second of a three-game series at Fenway Park.

"Matt Moore was really good," Rays manager Kevin Cash said. "Sometimes it's more beneficial to see a guy that comes out of the gate, struggles for him individually, to be able to work through that. That was really nice to see."

Moore wound up allowing two runs on seven hits while striking out seven.

Moore, an All-Star and 17-game winner in 2013, has strung together back-to-back starts of at least six innings, including a seven-inning no-decision against the Baltimore Orioles on Thursday. The two-start stretch is the southpaw's best since he returned from Tommy John surgery on July 2.

"I think it's very important," said Moore, who missed more than a year after having the season-ending operation in April 2014. "If we can just stay where we're at right now and just continue to make pitches when I have to, I think I should be all right heading into the winter."

It was a far better result for Moore than his Aug. 1 outing at Fenway Park, when he was shelled for six runs over three innings in a loss, his third in as many starts. Moore, who hopes to make two more starts before the season ends, is now 2-4 with a 6.48 ERA.

"We want all of our players to finish on good notes, strong notes," Cash said, "but I think ... for him to be able to go into the offseason knowing that he's back, that he feels really good, that will be a big boost for him going into the offseason and then carrying that into next year."

Evan Longoria's sacrifice fly in the sixth inning resulted in the tying and go-ahead runs crossing the plate for Tampa Bay (73-78), which reclaimed fourth place in the AL East. The Rays fell into last place after an 8-7 loss to the Red Sox on Monday.

The Rays third baseman lofted a ball to deep right field with two outs in the sixth Tuesday, and designated hitter Richie Shaffer tagged from third to tie the game at 2-2. Left fielder Brandon Guyer also scored as Red Sox right fielder Mookie Betts' throw sailed over the catcher and out of play.

Mikie Mahtook put the game out of reach with a two-run home run in the eighth, as the Tampa Bay center fielder launched a pitch over the Green Monster in left to make it 5-2.

Tampa Bay right fielder Steven Souza Jr. also drove in a run on a fifth-inning sacrifice fly.

Rays right-hander Brad Boxberger pitched a scoreless ninth inning for his 36th save.

Boston (72-78) had its three-game winning streak snapped and returned to the AL East cellar.

Red Sox left-hander Henry Owens (3-3) surrendered all five runs, four of which were earned, on seven hits in 7 1/3 innings. He walked two and struck out five.

"I think Henry Owens has gotten us deep into games and helped us win games, and I thought he deserved opportunity tonight," Red Sox interim manager Torey Lovullo said. "I don't think I could have slept tonight if we took him out of the game."

Owens, who held the Rays hitless through four innings before second baseman Logan Forsythe's leadoff double in the fifth, had allowed just one run and recorded seven strikeouts in his past 13 innings entering Tuesday's game.

"I was a little overzealous at times," Owens said. "Efficiency was definitely there early, and you know, we came out strong early. We just have to keep the momentum on our side, get them back in the dugout and keep hitting."

Red Sox first baseman Travis Shaw drove in both of his team's runs with a double in the first inning, and shortstop Xander Bogaerts extended his hitting streak to 11 games with a leadoff double in the third.

Boston designated hitter David Ortiz, baseball's newest member of the 500-home run club, was 0-for-3 with a walk and is now hitless in his past 12 at-bats.

NOTES: Red Sox 3B Pablo Sandoval missed his second consecutive game with a severe upper-respiratory infection. He will miss a few more days, interim manager Torey Lovullo said. ... Rays CF Kevin Kiermaier was not in the lineup against a left-handed pitcher Tuesday. OF Mikie Mahtook started in center field and hit a home run. ... Tampa Bay shut down RHP Nathan Karns (forearm tightness) for the rest of the season. Karns and Rays manager Kevin Cash said the injury isn't serious. ... Red Sox RHP Rick Porcello (8-13, 5.16 ERA) opposes Rays LHP Drew Smyly (3-2, 3.64 ERA) on Wednesday in the series finale.