Fister (5-7) won for the fourth time in five outings, striking out nine while hurling 71 of his 109 pitches for strikes.
The right-hander worked around a pair of walks as the Tigers avoided a three-game sweep at the hands of the Blue Jays.
Peralta's three-run shot in the second erased an early 1-0 deficit and the Detroit shortstop added a bases-empty clout in the ninth to supply all of the Tigers' offense.
Second-place Detroit came into the contest trailing the American League Central-leading Chicago White Sox by 2 1/2 games.
Toronto's Brett Cecil (2-4) was tagged with the loss, surrendering three runs on four hits over 6 2/3 frames.
Colby Rasmus drove in the Blue Jays' only run.