Paul Byrd (4-10) allowed one run on nine hits with five strikeouts in 5 1/3 innings to get his first win since June 6.
Rafael Perez allowed one run in 2 2/3 innings in relief of Byrd, and Masahide Kobayashi struck out the side in the ninth to pick up his sixth save of the season for Cleveland, which won its third straight and its seventh out of eight.
Grady Sizemore doubled and scored a run for the Indians.
LA starter and loser Ervin Santana (11-4) allowed four runs on seven hits with eight strikeouts in seven innings.
Howie Kendrick had three hits, including a solo homer for the Angels, who left nine men on base and lost for the first time in six games.