Anderson (5-7) struck out nine and walked two.
Nomar Garciaparra returned to Boston for first time since the Red Sox traded him to Chicago July 31, 2004. He was 2-for-4 with an RBI for the Athletics, who have won three of their last five games.
Jason Bay and Nick Green had the only hits for the Red Sox, who have lost three of four.
John Smoltz (0-2) made his Fenway Park debut as a member of the Red Sox and gave up five runs on 10 hits in six innings.