The Blue Jays were mathematically eliminated from the playoff race with the loss.
Victor Martinez also homered for Boston.
Lester (18-8) won his fifth straight start and became the first Red Sox lefty to win 18 games since Bruce Hurst in 1988. Lester pitched out of bases-loaded jams in the third and fifth, allowing four hits and four walks in all.
He struck out only four, snapping a string of four straight games in which he'd fanned at least 10.
Shaun Marcum, who hadn't allowed more than three runs in an outing in six starts, lasted 5 1/3 innings for Toronto and gave up six runs on nine hits while striking out three. It was his worst start since he allowed eight runs, including a career-high four homers, to the Red Sox on Aug. 11.
Marcum (12-8) gave up Martinez's solo homer in the fourth, then got into real trouble in the fifth when Jed Lowrie and Bill Hall singled to start the inning and Daniel Nava followed with a ground-rule double over the short fence down the right-field line. Yamaico Navarro singled to left to score Hall, and Nava came in when left fielder Mike McCoy let the ball roll past him for an error.
One out later, Drew hit a two-run homer over the Red Sox bullpen to make it 6-0.
Jose Bautista went 0-for-4 and failed to homer for the first time in four games. He has a major league-leading 49 homers, the most in Toronto history.
Notes
The last AL pitcher to strike out at least 10 batters in five straight games was Johan Santana, with five in a row for Minnesota in 2004. Pedro Martinez was the last Red Sox pitcher to do it, whiffing at least 10 batters in five consecutive games in 2001. … The Red Sox made a game-time decision to rest third baseman Adrian Beltre, who rolled over his left wrist diving for a grounder on Saturday. … Toronto sat second baseman Aaron Hill for a second straight game. He left Friday's game after being hit by a pitch on his right wrist.