Sale (11-12) raised his season strikeout total to 207 with the performance, during which he controlled the hard-hitting Tigers on one run. The left-hander allowed four hits and one walk.
Paul Konerko's two-run single in the first inning put the White Sox ahead for good while Dayan Viciedo and Josh Phegley each added an RBI as Chicago claimed the first of a three-game series.
Scherzer (19-3), meanwhile, fell short in his bid for a 20th win for the third straight start, yielding five runs (four earned) on six hits over four full innings.
Victor Martinez went 2-for-3 with a solo homer for American League Central-leading Detroit.