Lonnie Chisenhall added two hits with an RBI and Michael Brantley knocked in the other run for the Indians, winners of five straight including the first two in this set.
Nick Hagadone (1-0) recorded the final two outs of the seventh, and fanned three over 1 1/3 scoreless relief frames for the win. Cody Allen turned in a scoreless ninth for his fifth save.
Xander Bogaerts finished 2-for-4 with a solo homer and two runs scored for the Red Sox, who have lost two in a row since winning seven straight. Dustin Pedroia and Jonathan Herrera contributed an RBI each in defeat.
Jake Peavy (1-3) surrendered all five runs on eight hits over 6 1/3 innings.