Encarnacion has seven homers in his last six games. He is the first Toronto player to have four multi-homer games in a month, and the first major-leaguer to do so since Troy Tulowitzki in September of 2010.
Drew Hutchison (3-3) allowed one run in 5 1-3 innings for Toronto, which has won seven of its last nine games. The Blue Jays have won three consecutive series. Casey Janssen pitched the ninth for his fifth save.
Xander Bogaerts had three hits, including two doubles, for Boston. Clay Buchholz (2-4) allowed four earned runs in 4 2-3 innings.
The Red Sox are in the midst of their longest losing streak since dropping the final eight games of the 2012 season, ending the Bobby Valentine era after one year.
The Blue Jays made it 4-0 after three innings thanks to Encarnacion, who hit a solo homer in the second and a two-run shot in the third - both of them into the seats above the Green Monster. Shane Victorino homered for Boston - his first since a Grand Slam in Game 6 of the AL championship series against the Detroit Tigers - to make it 4-1.
Dioner Navarro's RBI single in the fifth made it 5-1 and chased Buchholz. He allowed nine hits and two walks, striking out two. The Blue Jays added another run in the seventh on Anthony Gose's RBI single.
The Red Sox scored three in the eighth to make it a two-run game thanks partly to back-to-back RBI doubles by Mike Carp and Bogaerts. Brock Holt singled to score Bogaerts before Brett Cecil struck out Grady Sizemore and then Steve Delabar, on his first pitch, retired Dustin Pedroia on a groundout.