In Cleveland, Toby Harrah drove in three runs with a homer and a two-run single and Pat Tabler hit a two-run home run to help Rich Barnes earn his first major-league victory.
Harrah also scored the go-ahead run in the sixth inning to end a 6-6 tie against Doug Bird (1-4). Harrah drew a one-out walk, went to third on Bake McBride's single and scored when right fielder Rick Miller bobbled the ball for an error.
Barnes (1-0), who was recalled from Charleston earlier this week, took over for starter Rick Sutcliffe in the third inning. He allowed one run and five hits before Bud Anderson came on to get the final out for his seventh save.
The Indians took a 6-5 lead with a four-run third inning highlighted by Harrah's two-run single and Tabler's fifth homer of the season.
Carl Yastrzemski's RBI double tied the score at 6 for the Red Sox in the fourth.
Jim Rice hit his 35th homer, a two-run shot, in the first and Yastrzemski hit a two-run homer that completed a three-run third inning. Rice's sacrifice fly in the third brought home Jerry Remy, who had singled and advanced to third on Wade Briggs' single.