Masterson, 2-3, surrendered just five hits, striking out four and walking five in his first home stadium win of the season.
Vinnie Pestano pitched a scoreless eighth inning and Chris Perez gave up a single in the ninth in earning his 16th save as the Indians (26-18) improved to eight-games above .500.
Detroit's Justin Verlander (5-2) gave up a lead off home run to Shin-Soo Choo then settled down striking out seven with one walk over eight innings.
Jose Lopez hit an RBI single in the fourth accounting for the Indians' second run.
Miguel Cabrera hit a Masterson fastball off the top of the right field wall in the first inning for the Tigers but settled for a single and failed to score.
In the third inning, Quintin Berry doubled and scored on Cabrera's groundout for Detroit's lone run.