Jim Rice and Dave Stapleton hit bases-empty homers and Jerry Remy knocked in two runs in a game shortened to 5 1/2 innings by rain in Boston. It was Oakland's sixth straight loss, Boston's fifth victory in a row.
Dennis Eckersley (5-3) allowed only three hits in six innings. The game, which had been interrupted once by rain for 67 minutes in the second inning, was called after a 33-minute delay.
A's Manager Billy Martin, who said the game should never have been started because of the weather, said he planned to file a protest.
"I'm surprised Eckersley pitched as well as he did," said Martin angrily. "(Mike) Norris was all over the place."
The Red Sox reached A's starter Norris (2-4) for a run in the second inning. Rich Gedman singled, went to second when shortstop Tony Phillips bobbled Rick Miller's grounder and scored on Remy's single to center.
Rice led off the third inning with a homer and two outs later, Stapleton homered.
Boston scored its final runs in the fifth, aided by a wild pitch by Norris, a hit batsman and a wild throw by catcher Mike Heath.
The A's Rickey Henderson stole second as part of a double steal in the third inning, giving him 42 thefts in 43 games. He leads the league by 28.