Will Middlebrooks followed by blooping a pitch just inside the right-field line, scoring a pair of runs, and Ellsbury then made it 4-0 with an RBI double into the right-center field gap.
He later added another run-scoring two-bagger for the American League East-leading Red Sox, who rebounded after two straight losses in Kansas City.
Brandon Workman (3-1) notched the decision with 1 1/3 scoreless innings in relief of Felix Doubront and Koji Uehara picked up his 12th save for Boston.
The loss was hung on Royals' Jeremy Guthrie (12-8), who surrendered five runs on 10 hits over six innings.
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