Kazmir (2-1), who returned to the starting rotation after a brief stint in the bullpen, yielded just three hits while fanning a career-high nine batters and walking three.
Danys Baez worked the ninth and got his 27th save.
Pedro Martinez (16-6) took the loss after allowing two runs on three hits over six innings. Martinez, who had won three straight starts, struck out 10 and walked five.
Trot Nixon hit a two-run homer for the Red Sox, who entered the night three games behind the New York Yankees for first place in the AL East.
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