Cabrera, who went 5-for-5 with two homers and five RBIs on Sunday, drove his double off reliever Daniel Bard (1-4) to the wall in left field, scoring Michael Brantley and helping the Indians win their fourth straight and improve to 19-4 at home.
Cabrera also homered in the fourth, his third homer in two days.
Joe Smith (2-1) got one out in the eighth, and closer Chris Perez got Carl Crawford to bounce into a game-ending double play for his 13th save.
Trailing 2-1 and being held in check by Boston starter Clay Buchholz, the Indians came up with some more late-inning magic.
They tied it when Jack Hannahan singled, pinch-runner Adam Everett moved up on a groundout and scored on Brantley's two-out RBI single. The Indians then took the lead on Cabrera's double, yet another dramatic moment for the Indians at home. The game started after a 61-minute rain delay.
Cleveland became the first team in the majors to reach 30 wins, and the Indians gave a national TV audience a firsthand glimpse of what they've been doing all season. Manager Manny Acta wasn't around to see it after getting tossed in the eighth.
The loss could be doubly costly for the Red Sox.
Pedroia, the scrappy All-Star second baseman, injured his left leg when he fell over second base while trying to go to third in the eighth inning.
Pedroia was rounding second on Adrian Gonzalez's single to right, when he got his feet tangled up after hitting the bag. He fell awkwardly but was able to scramble on his belly back to the base safely. Pedroia laid with his face in the dirt as a team trainer and manager Terry Francona jogged out to check on the former AL MVP.
Pedroia got to his feet, but was in obvious pain. He then limped back slowly to Boston's dugout, accompanied by a concerned Francona.
The team had no immediate word on his condition.
Crawford homered for the Red Sox, who lost for just the second time in 10 games.
Buchholz allowed just two runs and four hits in 7 1/3 innings, but Bard couldn't hold back the Indians.
Boston was making its second visit to Cleveland this season. The Red Sox were swept in a three-game series in early April, dropping them to 0-6. But they've recovered from the awful start and are finally playing like the team many predicted would win it all in 2011 — just not against the Indians.
A major, $142 million-over-seven-years disappointment so far with the Red Sox, Crawford snapped a 1-1 tie in the fifth with just his second homer. He turned on a 1-1 pitch from Justin Masterson, driving it over the wall in right for his first homer since April 27.
As hot as any hitter in the game, Cabrera tied it 1-1 with his 10th homer. It was Cabrera's seventh straight hit, four shy of the team record held by Hall of Famer Tris Speaker in 1920. Cabrera flied out in the sixth to end his streak.
The Red Sox went up 1-0 in the third on a perfectly executed hit-and-run single by Pedroia.
Notes
Gonzalez is just the fourth Red Sox player since 1920 to have at least 65 hits and 40 RBIs through the club's first 40 games. The others: Ted Williams (1948), Jim Rice (1978) and Manny Ramirez (2001). Gonzalez came to Boston in a December trade from San Diego. "It's nice to see it in person," Francona said. "You make a trade of that magnitude, you've got a pretty good idea of what a guy can do, but when you see a really good hitter in the midst of a good streak, it is fun to watch." … The Indians said Cabrera on Sunday joined Cincinnati's Roy McMillan (1960) as the only shortstops since 1946 to go 5-for-5 with two homers and five RBIs in a game. Cabrera leads all AL shortstops in runs, hits, homers and RBIs.