Fister (6-7) dominated the Indians, tossing 73 of his 107 pitches for strikes en route to his fifth win in six starts.
The right-hander issued only one run, didn't allow a walk and struck out six while compiling the fourth complete game of his career.
Second-place Detroit came into the contest trailing the American League Central-leading Chicago White Sox by 2 1/2 games.
Indians starter Ubaldo Jimenez (8-11) was tagged for six runs on seven hits in a 5 1/3-inning stint.
Jason Kipnes got the RBI for the reeling Tribe, who dropped their eighth straight.