Greinke, with two complete-game victories over the Tigers this year, held them to three hits and struck out seven over seven innings. Washburn, making his third start in a Detroit uniform, surrendered three hits in eight frames.
Colon (1-2) worked a perfect eighth and came back in the ninth in hopes of getting the Royals into extra innings. After striking out Marcus Thames to open the ninth, however, Colon gave up Inge's homer to left on a 2-1 pitch. It was Inge's 23rd home run this year.
Brandon Lyon (6-4) worked a perfect top of the ninth for the victory.
Detroit, winners of two in a row, began the night with a 2 1/2-game lead over the Chicago White Sox in the American League Central.