Ross blasted a three run shot to tie the game and Lavarnway delivered the go-ahead solo homer two batters later to bring Boston's season-high seven-game losing streak to an end.
Blake Beaven (9-9) was charged with all four Boston runs. He allowed eight hits over 5 2/3 innings.
Seattle took a 3-0 lead into the sixth thanks to an RBI single by Jesus Montero in the first inning and solo home runs by Franklin Gutierrez and Kyle Seager in the third.
The Mariners outhit the Red Sox 12-10.