Colabello, who entered the day tied for the AL lead in RBIs with seven, added four more to give him 11 on the year, including a go-ahead three-run double in the sixth inning.
"It was a good win today -- a good battle," Twins manager Ron Gardenhire said. "The guys were really competing and kept getting after it. Our starter wasn't able to get the ball where he wanted to. It was up and a little bit of a struggle for him. But our bullpen came in, and most of our guys came in did what they were supposed to do and got outs."
It was a wild game that saw the Twins chase Indians right-hander Justin Masterson after just 3 2/3 innings, as he gave up six runs (five earned) on seven hits and three walks.
The Twins scored twice in the second with Kurt Suzuki driving home a run with a single to right before Aaron Hicks grounded into a run-scoring double play.
They added three more runs in the third, keyed by a throwing error from Indians catcher Yan Gomes on a weak grounder hit by Colabello with two on and one out. Gomes threw to second with nobody covering, which allowed Brian Dozier to score with the ball skipping into the outfield. Trevor Plouffe promptly laced an RBI single to left, before Jason Kubel hit a grounder under the glove of Jason Kipnis at second for an RBI single of his own.
"We got lucky a few times out there with some rollers," Gardenhire said. "We hit some balls at them, and they hit some rockets at us. So sometimes luck goes your way. But we're competing really well out there and it's fun to see."
Colabello helped the Twins to a four-run cushion with an RBI single in the fourth that knocked Masterson out of the game.
"He just wasn't commanding," Indians manager Terry Francona said of Masterson. "He's falling behind on some hitters -- ball one, ball two, ball three. He hit a couple guys, right-handed hitters. He was just letting a couple fly arm-side. And his breaking ball, he swept a lot of them out of the zone. It was just hard for him."
But the lead wasn't to be, as Nolasco struggled in his second start of the season. He gave up a two-run homer to Gomes in the second before giving up three more runs in the fourth, after the Twins didn't turn what could've been an inning-ending double play on Mike Aviles.
Nolasco wasn't helped by his defense in the fourth, his final inning, as Jason Bartlett had trouble with a ball hit off the left-field wall by Kipnis with two outs. Bartlett, making just his second career appearance in left field after Josh Willingham exited the game in the second with a bruised left wrist, misjudged the ball off the wall and couldn't handle the carom, allowing three runs to score.
"It was just a terrible day in general," Nolasco said about his outing. "I thought I did a good job battling for a few innings, but it got away from me in the fourth. But I thought the guys did a good job battling and scoring runs there to come back on top."
Right-hander Anthony Swarzak replaced Nolasco in the fifth, as Nolasco gave up five runs on seven hits and four walks to see his ERA rise to 9.00 on the season.
Swarzak gave up a run in the fifth to tie the game at 6 with Bartlett struggling defensively again, as he couldn't handle a sinking liner from Lonnie Chisenhall to open the inning, and it went off his glove for a double. Chisenhall then scored on an RBI double from David Murphy, despite a diving attempt from Bartlett down the left-field line.
But Colabello gave the Twins the lead for good with a three-run double to deep left field off reliever Blake Wood with the bases loaded and one out in the sixth.
"I was just trying to hit in the air," Colabello said. "In an at-bat like that, I just try to remind myself the pitcher is up against the wall. So I tried not to do too much and put a good swing on the ball."
Hicks added an insurance run for the Twins when he plated Plouffe with a sacrifice fly in the ninth. Francona challenged the call, but Plouffe was confirmed safe on instant replay.
The Indians threatened with a run in the sixth with three straight singles off Swarzak to chase him from the game. But Caleb Thielbar, Casey Fien, Jared Burton and Glen Perkins combined to shut down the Indians, despite a few scares over the final 3 2/3 innings, to preserve the victory for the Twins, who won their first series of the year to finish 3-3 on the road trip.
"I thought we had some good wins, some character wins," Colabello said. "If you look back, you could say we even had a chance to be 6-0. But you'll definitely take a .500 road trip to open the year, and we look forward to going home and playing in front of our home crowd."