Ellsbury hit a two-out homer off Joe Smith Wednesday after delivering an RBI single in the ninth that gave the Red Sox the victory Tuesday.
Boston never trailed, but Cleveland twice came back to tie it. Ezequiel Carrera rallied the Indians into a 3-3 deadlock in the seventh with a ground-rule double that scored Lonnie Chisenhall.
Boston closer Jonathan Papelbon (4-0) came on in a tie game in the ninth and got the win with a perfect inning.
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