Anderson (3-0) notched his third consecutive win since making his 2012 debut following elbow ligament replacement surgery, stifling the Red Sox on one run through six innings.
The left-hander issued one walk and stuck out four as the American League wild card-leading A's completed a three-game sweep of Boston and extended their longest winning streak since 2006.
Josh Reddick and Yoenis Cespedes also provided RBI in the victory.
Boston's Daisuke Matsuzaka (1-4) was rocked for six runs on seven hits in a 3 2/3-inning effort.
Cody Ross and Mauro Gomez each drove in a run for the Red Sox.