Fister (10-9) scattered seven hits, didn't issue a walk and struck out seven, hurling 76 of his 117 pitches for strikes.
The right-hander retired 14 of the last 15 batters he faced for the second-place Tigers, who came into the contest trailing the American League Central-leading Chicago White Sox by 1 1/2 games.
Miguel Cabrera socked a solo homer -- his 42nd of the year, tying him with Josh Hamilton of the Texas Rangers for the major-league lead. He also came into the game leading the American League in batting average and RBI.
Twins starter Samuel Deduno (6-5) was rocked for seven runs on seven hits in just 2 1/3 innings.