Boston (25-16) now stands a half-game back of the front-running Jays (27-17).
"They came in feeling really good about themselves, as they should," Francona said. "They've got a good team. But we did what we were supposed to do, what we hoped to do."
Jason Bay belted his team-leading 13th home run of the season for the Sox, who greeted Toronto rookie right-hander Robert Ray (1-2) with a three-run first inning and never looked back.
After David Ortiz knocked in Jacoby Ellsbury with a groundout to the right side of the infield, Bay clubbed a 3-1 fastball deep to right field, off the top of the wall and into the seats above the Red Sox bullpen.
"For right-handed hitters, hitting the ball in the bullpen is not an easy thing to do," Francona said. "I know where the ball hit, but to hit it that far, he's got some strong wrists on him."
Each of Bay's past 11 home runs has come with at least one runner on base, a single-season franchise record. If his next homer comes with one or more runners on, he will tie noted sluggers Hank Aaron (1970) and Ken Griffey Jr. (1990) for the all-time Major League mark.
Each of Jason Bay's past 11 home runs has come with at least one runner on base, setting a club record. Here is Boston's leaderboard in the category.
Information courtesy of David Vincent from the Society of American Baseball Research.
The Sox tacked on runs in the third and fifth innings, thanks in large part to the efforts of Dustin Pedroia. The reigning AL MVP demonstrated his trademark grit in the bottom of the third, diving into second base for a double after driving a fastball off the Green Monster. He scored two batters later on Kevin Youkilis' single to center field.
Lester's most daunting obstacle came in the fourth inning, when he wiggled out of a two-on, one-out situation by inducing a 4-6-3 double-play ball off the bat of Jose Bautista.
"It definitely boosts your confidence," Lester said of the double play. "You execute the pitch, you get ahead of the guy, and you get the result you want. Sometimes it just doesn't happen, so for that to happen tonight was big."
The escape act preserved a 4-0 lead for the Sox, who improved to 15-2 in their past 17 home games.
Boston stretched its lead to 5-0 in the fifth, when Pedroia rewarded Ellsbury for swiping his 17th base of the season by knocking in the speedster with a single to center.
Despite peppering Lester with eight hits, the Jays were held scoreless until Aaron Hill's seventh-inning RBI single off Ramon Ramirez.
One week after vowing to put his recent struggles behind him, Lester looked much more like last year's 16-game winner against a Toronto offense that led the Majors in runs scored heading into its series with Boston.
"I just wanted to make sure that everybody knew I'm not throwing in the towel," said Lester, who improved to 3-4. "It's a long season. You're going to have some bumps in the road, and sometimes those bumps are pretty deep and you've got to dig yourself out of them.
"Tonight was definitely a step towards getting out of that hole."