Jason Kipnis and Lonnie Chisenhall each hit solo homers off Red Sox starter Josh Beckett, but Boston scored a run the ninth inning to beat the Tribe 3-2.
Jacoby Ellsbury had the game-winning single, scoring Jared Saltalamacchia off of Indians reliever Vinny Pestano to give the Red Sox the victory. The Red Sox had three straight singles off Vinny Pestano in the ninth, who was saddled with the loss.
David Huff started for the Indians, giving up only one run, which was unearned. Huff was then sent back to Columbus after the game to make room for newly acquired starter Ubaldo Jimenez.
The Indians and Red Sox will resume their four-game series on Wednesday at 7:10 p.m.