Correia (7-6) yielded three hits, issued one walk and struck out three, exiting with the Twins trailing 2-0.
Minnesota, however, struck for three runs in the bottom of the sixth, triggered when Indians third baseman Lonnie Chisenhall threw wildly to home on Ryan Doumit's grounder, allowing Joe Mauer to score from third.
Colabello, playing in his ninth major league game, followed by blooping a hit to right off Rich Hill (1-2), chasing home Justin Morneau with the score-tying run.
Bryan Shaw took mound, striking out Aaron Hicks for a first out, but the Twins grabbed the lead when Clete Thomas drove in Doumit on a fielder's choice grounder.
Jason Kipnis went 2-for-4 with a two-run homer for the Indians, who remained 1 1/2 games behind American League Central-leading Detroit.
2014: The Year in Music [PHOTOS]