It was Detroit's fourth win in a row.
Placido Polanco's two-run fifth-inning double started the scoring.
One of three hits by Miguel Cabrera was a solo sixth-inning homer.
Galarraga (2-0) gave up the four hits in 6 1/3 innings with two walks and five strikeouts.
Relievers Bobby Seay, Ryan Ferry and Fernando Rodney completed Detroit's first shutout this season.
Four players had one hit for the White Sox, whose three-game winning streak ended.
Losing pitcher Jose Contreras (0-2) yielded five runs -- four earned -- and five hits in 5 1/3 innings.