BOSTON — Randy Arozarena misplayed J.D. Martinez’s fly ball into a two-run double with two outs in the bottom of the 12th inning, lifting the Boston Red Sox over the Tampa Bay Rays 6-5 on Tuesday night.

The Rays were in line for the win before Christian Vázquez belted Diego Castillo’s 0-2 pitch over the Green Monster for a tying homer leading off the ninth.

Martinez had an RBI double in the eighth for the Red Sox, who won their second straight after an 0-3 start.

Manuel Margot hit a two-run single for the Rays, who wasted a strong six-inning effort by starter Tyler Glasnow. Tampa Bay lost the series opener 11-2 on Monday night and has dropped three in a row.

With runners on second and third after a wild pitch by Ryan Thompson (1-1), Martinez hit a fly ball to right. Arozarena twisted around and made a dive back toward the wall as the ball fell over his head for the winning hit.

Phillips Valdez (1-0) got the victory.

Arozarena’s grounder had driven in Mike Zunino in the top of the inning.

Each team drove in their placement runner with a leadoff hit in the 11th.

Coming off six scoreless innings in his first start of the season when he gave up just an infield hit, the hard-throwing Glasnow struck out nine and allowed one run on four hits with two walks. He permitted his only run on a wild pitch in the first.

Boston starter Martín Pérez gave up three runs on five hits, striking out six and walking two in five innings. He was pulled after walking the leadoff hitter in the sixth.

The Rays jumped ahead 2-1 on Margot’s bases-loaded single in the third that snuck between first baseman Marwin Gonzalez’s dive and past second baseman Christian Arroyo.

NOTES: Boston LF Franchy Cordero made a leaping catch at the Green Monster with runners on first and second with one out. As he made the grab, his glove smacked the wall, sounding as though the ball hit the Monster. Cordero fired to second because the runners had advanced thinking the ball was in play, so shortstop Xander Bogaerts stepped on the bag. Third-base umpire Dan Iassogna ruled a catch and replay upheld the call, so the double play stood, too. … Manager Alex Cora said LHP Eduardo Rodriguez (left elbow inflammation) will come off the IL and start the series opener in Baltimore on Thursday. Asked if there were any pitch counts, Cora said: “There’s no hard number. He’s going to go deep into the game.”