Toronto scored the game's first five runs, then fought off a Boston charge thanks, in part, to a two-run homer by Colby Rasmus in the ninth inning.
Boston lost for the 10th time in 11 games.
Encarnacion had a sacrifice fly in the first inning and hit a solo shot in the third, his 38th homer of the year. Sierra delivered a two-run blast in the fourth.
Boston closed within 5-2 heading into the ninth, but the homer by Ramus gave the Blue Jays plenty of cushion heading into the bottom of the inning.
Mauro Gomez then hit a two-run home run for the Red Sox to complete the scoring.
Henderson Alvarez (8-12) worked 6 1/3 innings to get the win, giving up two runs on four hits. Toronto got to Felix Doubront (10-8) for five runs on six hits in four innings.
Celebrity Families of 2014 [PHOTOS]