Haren (1-1) collected his first victory in his fifth start to begin the season, yielding one run while holding the Indians to four hits and two walks. He struck out seven.
The right-hander has allowed only four runs over his last 22 innings for Los Angeles, reducing his ERA to 3.34 in a game that was delayed more than 2 hours by rain.
Scott Downs racked up his first save of the season with a 1-2-3 ninth as the Angels evened their three-game set with Cleveland.
Tribe starter Jeanmar Gomez (1-1) absorbed the loss, allowing two runs on five hits in a six-inning effort.
Jack Hannahan drove in the Indians' only run.
Celebrity Families of 2014 [PHOTOS]