Nick Swisher belted a solo homer as Cleveland took the opener of a three-game series.
Zach McAllister (6-7) allowed just one run for a second straight start, taming the Angels on five hits and two walks through 6 1/3 innings. The right-hander struck out five.
Los Angeles starter Jered Weaver (7-7) was reached for four runs on eight hits in a six-inning performance.
Mark Trumbo socked a bases-empty homer and finished with two RBI for the Angels.