Drew, who hadn't played since July 19 due to a left shoulder impingement, was hitting seventh in the lineup. He went 1-for-5 with an RBI.
The victory moved the Red Sox to a one game lead on the Tampa Bay Rays for the wild card spot.
Drew has batted .218 with just four home runs, six doubles and 22 RBI over 78 games this season.
The Red Sox also recalled outfielder Ryan Kalish from Pawtucket and placed him on the 60-day disabled list. He had neck surgery September 14.