BOSTON -- Xander Bogaerts was guilty of a seventh-inning throwing error that could have been costly on Monday night.

But the shortstop more than made up for it.

After the error wound up not hurting the Red Sox, Bogaerts doubled home a run in the bottom of the inning and then hit a grand slam with two out in the eighth to give Boston a wild 8-7 win over the Tampa Bay Rays in the opener of a four-game series.

“It’s just nice to contribute with the team and help us win,” said Bogaerts, who has had a Gold Glove-type season in the field. “I threw away that ball in the seventh inning and I was really mad.”

The win, which moved the Red Sox out of the American League East cellar past the Rays, came on a night when both teams were officially eliminated from winning the division -- by virtue of the Toronto Blue Jays' victory over the New York Yankees. Both Boston and Tampa Bay are technically alive in the AL wild-card chase.

But even though this game really didn’t mean much, it was a crazy affair that included four replays, two in the top of the first inning.

The win was Boston’s third straight and also moved the Red Sox to within a game of the third-place Baltimore Orioles.

“We really [came back] two times and the second time was a little more special because it happened with two outs,” said interim manager Torey Lovullo, 22-13 running the club while John Farrell receives treatment for lymphoma. “Xander came through with the big hit, which capped a really big night.”

Bogaerts connected on a 2-2 pitch from Brandon Gomes (2-6) for his first career grand slam, capping his career-high, five-RBI night.

Tampa Bay (72-78) led 3-1 before the Red Sox scored three in the seventh. The Rays came right back with three in the top of the eighth before Boston struck again to win its third straight and get to within five games of the .500 mark for the first time since July 12. The Red Sox (72-77) are a game behind the Baltimore Orioles for third place.

This is the latest in a season the Rays are in last place since the Devil Rays did it in 2007.

Left-hander Xavier Cedeno struck out the first two batters in the bottom of the eighth but then hit center fielder Jackie Bradley Jr. with a pitch. Gomes came on and gave up a single to right fielder Mookie Betts before second baseman Dustin Pedroia reached on his third hit of the night, a single to deep short.

Bogaerts, who now has 78 RBIs on the season, then came through with his seventh homer.

“I went back and looked at the home run pitch — it was actually a halfway decent pitch,” said Gomes. “He just put a good swing at it.”

Right-hander Jean Machi (1-0) got the win after retiring the only two batters he faced. Left-hander Robbie Ross Jr. recorded his third save in as many days, his fifth of the season, but allowed a solo homer to designated hitter Richie Shaffer before ending it.

Outfielder Grady Sizemore, who came on as a pinch hitter in the seventh inning, doubled home two runs in the three-run eighth that gave the Rays the lead. Second baseman Logan Forsythe, who had an RBI single in a three-run first inning, capped the rally with a sacrifice fly.

“Frustrating loss,” said Rays manager Kevin Cash. “Interesting game to say the least. A lot of good things. A lot of negative things.”

Neither starting pitcher was involved in the decision. Tampa Bay's Chris Archer pitched five innings of one-run ball, throwing 99 pitches and walking five, while Boston's Eduardo Rodriguez allowed three runs in six innings, all the runs scoring before Rodriguez got an out.

Outfielder Brandon Guyer led off the game with a home run and paced the Rays with three hits.

NOTES: Former teammates Pedro Martinez, Tim Wakefield and Jason Varitek were on the field for pregame ceremonies honoring David Ortiz's 500th home run. Ortiz reached 500 with a pair in a game at Tampa Bay on Sept. 12. Tom Brady was one of the video messages delivered to Ortiz during the game. … OF Daniel Nava, who was on the 2013 World Series-winning Red Sox, returned for the first time and was given a video tribute in the second inning. Before the game, he said, "I didn't know where to go," when he entered the ballpark. ... Rays LHP Jake McGee, rehabbing from August knee surgery, will throw a simulated game at Fenway Park on Wednesday. He hopes to be available to pitch for Tampa Bay on Saturday. ... Rookie LHP Henry Owens goes for the Red Sox against LHP Matt Moore in Tuesday night's second game of the four-game series.