ST. PETERSBURG, Fla. -- Down 5-1 in the sixth inning and in danger of a fifth straight loss, the Tampa Bay Rays rallied for a 7-5 win over the Boston Red Sox on Wednesday night at Tropicana Field.

The Rays (7-8) tied the score with four runs and five singles in the sixth inning, then jumped ahead in the seventh on a double-play groundout and a solo home run by outfielder Jake Elmore in his first Rays at-bat.

Boston (9-6) saw the Rays load the bases in the sixth with consecutive singles by shortstop Asdrubal Cabrera, third baseman Evan Longoria and left fielder Desmond Jennings. Rookie first baseman Allan Dykstra, hitting .074, came through with an RBI single and second baseman Logan Forsythe followed with a bases-loaded walk.

Rays rookie manager Kevin Cash inserted Elmore as a pinch-runner at second, and when pinch-hitter Brandon Guyer singled, Elmore slid into home to beat the tag and score the tying run.

Tampa Bay again saw Cabrera and Longoria single to lead off the seventh, with Cabrera hustling to third on Longoria's hit. Jennings hit into a double play, but Cabrera scored for the lead, with Elmore making it a two-run lead with a solo home run. He became the 11th player ever to hit a home run in his first Rays at-bat. Cash did the same as a player in 2005.

Rays right-handed reliever Steve Geltz pitched a scoreless ninth and became the fourth Tampa Bay pitcher to post a save this season.

The Rays' No. 3 through 6 hitters -- Cabrera, Longoria, Jennings and Dykstra -- all came in batting below .200 for the season but went a combined 7-for-14.

Rays rookie outfielder Steven Souza, who hit a first-inning home run and later doubled, left the game after the sixth inning with a right forearm cramp after he struck out to end the inning.

Boston didn't get to Rays starter Nathan Karns often in the first early innings, but the Red Sox built a 4-1 lead thanks mostly to crushed home runs from second baseman Dustin Pedroia and designated hitter David Ortiz.

Pedroia's fourth homer of the season, a two-run shot after center fielder Mookie Betts walked, gave Boston a 2-1 lead in the third. The Red Sox added a run in the inning when catcher Mike Napoli ripped an RBI single off Karns' glove and into center field.

Ortiz added a huge solo home run to right field in the fifth, his third of the year. The Red Sox followed with a single from left fielder Hanley Ramirez and a ground-rule double from Napoli, putting runners at second and third with one out, but Karns got out of the jam to trail 4-1.

Tampa Bay, shut out twice in the previous three games, got a run in the top of the first when Souza hit a solo home run to left field, his fourth of the year. Souza added a double in the third, but the Rays couldn't move him around.

NOTES: The Rays have a team-record and major-league-high 11 players on the disabled list after adding 2B Ryan Brett, who dislocated his left shoulder Tuesday. ... Tampa Bay called up versatile INF Jake Elmore from Triple-A Durham. The 27-year-old has a .221 career average in 221 career games, most recently with the Reds in 2014. ... To make room on the 40-man roster for Elmore, the Rays shifted LHP Jeff Beliveau to the 60-day DL. He will undergo surgery Thursday to repair a torn left labrum in his throwing shoulder. ... Tampa Bay LHP Drew Smyly, yet to pitch in the majors this season because of shoulder tendinitis, will make his 2015 debut Friday with a home start against the Toronto Blue Jays. ... Only once in Boston's first 15 games did the opposing team record a quality start. That was by Philadelphia Phillies RHP Aaron Harang on April 8.