Fister (9-8) yielded a pair of runs on just two hits for the second-place Tigers, who cut Chicago's lead in the American League Central to two games while taking the second contest of a key four-game series.
The right-hander walked two and struck out six en route to his second win in two starts.
Jose Valverde secured the victory with his 29th save.
The Tigers erased a 2-0 deficit in the fifth when Austin Jackson clubbed a two-run homer and Cabrera followed one out later with a solo shot.
Chicago's Jake Peavy (10-11) yielded three runs on six hits over 5 2/3 innings.
Dewayne Wise and Gordan Beckham went deep for the White Sox.
Celebrity Families of 2014 [PHOTOS]