Jose Bautista added a two-run shot, his MLB-best 24th home run of the season, and J.P Arencibia contributed a two-run clout as well for Toronto, which banged out 13 hits to open a three-game series.
The game was delayed 1 hour, 56 minutes by rain in the top of the seventh inning at Fenway Park.
Henderson Alvarez (4-6) started and allowed five runs (three earned) on six hits to earn the win before coming out with elbow soreness in the sixth inning.
Boston starter Felix Doubront (8-4) was knocked around for seven runs (five earned) on 11 hits in over six frames.
David Ortiz connected for two home runs for the Red Sox.