It came despite trailing by four runs early and three errors, including a crucial dropped popup in foul territory by first baseman Justin Morneau with two outs in the third inning. Carl Crawford delivered a three-run homer on left-hander Brian Duensing's next pitch.
"Every win's big, but that might be one of the happiest wins we've had this year," Morneau said. "That could have been a real bad night if we didn't come back to win that game. We haven't played as well as we can this year, but I think it shows a lot about the character of this team. We get down and make some errors like we did and come back on a guy who's got a chance to be a good pitcher. It doesn't matter what our record is, we're still out there battling every day."
The game was ultimately won on Carroll's clutch single into center field off reliever Vicente Padilla that scored Darin Mastroianni, who led off the inning with a double to right-center. It was an impressive night for the second baseman, who went 4-for-4 with a double and a walk.
"I was trying to hit the ball hard and compete," Carroll said. "He threw a sinker that came over the plate and I was lucky enough to get it over [Red Sox second baseman Dustin] Pedroia's head and Masty scored. He had a great at-bat to get to second."
It came after the Twins rallied from an early four-run deficit. Duensing pitched well, but was hurt by the costly error from Morneau in the third.
Duensing appeared to get out of a big jam with two runners on and two outs by getting Crawford to pop up into foul territory. But Morneau dropped the pop fly and Crawford drilled a three-run homer on the very next pitch to give the Red Sox a 5-1 lead.
"That's probably the most embarrassed I've ever been on a baseball field," Morneau said. "I thought I could probably fit under first base if I could crawl under there. But I've got to give our pitching staff credit because they gave us a chance to win that game."
It was the third homer of the year for Crawford, who also scored in the second when he doubled and came around on a single from Kelly Shoppach. Adrian Gonzalez brought home a run in the third before Crawford's homer on an RBI single.
So while Morneau's error was costly, he did his best to make up for it at the plate by going 4-for-4 with two doubles.
His first double came against left-hander Felix Doubront in the second and he scored on a single from Mastroianni with the infield in.
Minnesota rallied to tie it with four runs in the fifth. Josh Willingham brought home the first run with a bases-loaded walk before Morneau plated two runs on a single to center field. Danny Valencia tied the game with a sacrifice fly to right field.
"We kept getting after it," Twins manager Ron Gardenhire said. "We got back in the game with some big hits and some big at-bats."
It handed Duensing a no-decision, as the left-hander ended up giving up five runs (two earned) on 10 hits over six frames.
"It was a little bit of a dog fight today," Duensing said. "I was fighting myself early. The ball was up today. It didn't have the same sink it had against Cleveland."
Relievers Casey Fien, Alex Burnett, Tyler Robertson, Jeff Gray and Jared Burton combined for four scoreless innings to preserve the victory. Burton picked up his fourth save with a scoreless 10th.
"Later in the game, we couldn't do it," Red Sox right fielder Cody Ross said. "Got to give them credit for their bullpen, their bullpen came in and did a great job."