Josh Willingham and Ryan Doumit (3-for-3) also provided run-scoring hits in the four-run rally, which erased an early 1-0 deficit, while Joe Mauer and Justin Morneau added RBI hits in next frame as Minnesota built a 6-1 advantage.
The Tigers came back with three runs against Twins starter Liam Hendriks and Anthony Swarzak (2-4) came in to toss 2 2/3 scoreless frames in relief to pick up the victory.
Alex Burnett fired 1 1/3 shutout frames and Glen Perkins earned his third save despite yielding a pair of hits in the ninth as Minnesota took the opener of a four-game series.
Doug Fister (1-6) lasted only four innings for the Tigers, surrendering six runs on eight hits.
Miguel Cabrera went 3-for-3 with a two-run double and a sacrifice fly for the Twins.