Colabello's solo shot in the fourth with the Twins trailing 6-2 began a long comeback that eventually saw Minnesota tie the game 6-6 on Pedro Florimon's eighth-inning RBI single.
In the ninth, Minnesota loaded the bases with two out against Chia Jen Lo (0-3) and Colabello followed by pounding a pitch over the right field fence for the go-ahead grand slam, finishing with five RBI.
Trevor Plouffe and Brian Dozier also each went deep for Minnesota, which took the first of a three-game series.
Josh Roenicke (3-1) got the win after starter Andrew Albers was lit up for five runs over just 1 2/3 innings.
Jose Altuve went 4-for-5 with an RBI while Jason Castro and Chris Carter each knocked in a pair for the Astros.