Fister (6-4) took a no-hitter into the sixth inning, eventually allowing just two hits and two walks and striking out seven in his first victory since May 14.
Joaquin Benoit earned his fourth save after blanking the Twins over the final 1 1/3 innings.
Hunter launched a two-run homer in the first inning, giving Detroit a quick lead, and added a RBI double in the ninth to cap the scoring as the American League Central-leading Tigers took the rubber match of a three-game set.
Austin Jackson also knocked a two-run homer for Detroit.
Minnesota starter P.J. Walters (2-2) was touched for four runs on nine hits in a 5 1/3-inning effort.
Brian Dozier went 2-for-3 with a solo homer for the Twins.