Mike Napoli added a pair of run-scoring singles for American League East-leading Boston.
Ryan Dempster (5-8) corralled the victory, allowing two runs on six hits over six innings.
Rockies starter Juan Nicasio (4-4) was rocked for seven runs (six earned) on 12 hits over just 2 1/3 innings.
Wilin Rosario went 3-for-4 with a solo homer for Colorado.
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