Quintana (6-4) held the Tigers to a single run on seven hits, walking two en route to the victory. The rookie left-hander located just 68 of his 112 pitches for strikes.
The next batter -- A.J. Pierzynski -- followed with a solo shot.
The American League Central-leading White Sox began a key four-game series with a victory that increased their lead over second-place Detroit to three games.
Porcello (9-12) surrendered four runs (three earned) on five hits over 5 1/3 innings, walking one and striking out four.
Jhonny Peralta drove in the Tigers' only run.