A sacrifice fly by Dane Sardinha sent home the other run for Detroit, which took two games in a three-game series.
Winner Armando Galarraga (3-0) pitched six innings, yielding a run and three hits and striking out seven batters.
Mike Aviles slugged a solo homer and Jose Guillen singled in the other run for Kansas City.
Sidney Ponson (0-3) was the losing pitcher, giving up three runs and six hits over eight innings. Ponson also had seven strikeouts.