Masterson (9-10) allowed six hits and three walks but benefited from three double plays turned by the Indians' infield. The right-hander struck out four.
Chris Perez racked up his 32nd save as the Tribe took the opener of a three-game series.
Lillibridge's solo shot in the fourth inning handed Cleveland a 3-0 lead. The Indians infielder also scored three times. Jason Donald added an RBI.
The loss was hung on C.J. Wilson (9-9), who surrendered three runs (two earned) on six hits in an 6 2/3-inning outing.
Albert Pujols socked a two-run homer for Los Angeles, which fell for the ninth time in 12 games.