"He got pretty close," Middlebrooks added. "I didn't know if he was going to make it. I was trying to time it out of the corner of my eye. I was like 'Am I going to have to shake this guy's hand?'"
Middlebrooks, who doubled and scored in the third, flied out to the left field warning track in his final at-bat in the eighth.
"I was blowing on it running down the line but it didn't have enough steam," he said.
Limited to 75 games as a rookie because of a broken right hand, the Red Sox have high hopes for Middlebrooks this year, his second big league season.
"We're counting on him to be a big run producer," former MVP Dustin Pedroia said. "He's got that ability."
Nava went back-to-back with Middlebrooks in the seventh, a homer that bounced off the top of the wall in center field and went out. It's the first time this season the Red Sox have hit consecutive home runs.
Ellsbury had three hits, including a leadoff homer into the second deck in right in the eighth, his first. Three batters later, Napoli capped the rout with a home run to center, his second. He finished with four RBIs.
Boston jumped on Dickey in the first, scoring five runs before the knuckleballer had recorded an out.
Ellsbury led off with a double, Shane Victorino singled to center and Pedroia drove in a run with a groundball single through the right side.
Napoli hit a two-run double and Middlebrooks followed with a first pitch homer to right.
Even the outs Dickey got were loud. Nava and Jarrod Saltalamacchia each flied out to the warning track before Jackie Bradley Jr. struck out to end the inning.
Dickey (0-2) allowed eight runs -- seven earned -- and 10 hits in 4 2-3 innings. It was his shortest start and the most runs he'd allowed since giving up eight runs in 4 1-3 innings of a 14-6 loss at Atlanta last April 18, when he pitched for the New York Mets.
"Throughout the course of the season you're going to have a clunker or two," Dickey said. "You just have to try and forget it as soon as you can. Obviously today was one of those days for me."
The five first inning runs allowed by Dickey matched the amount he gave up in the first inning in all of 2012, when he made 33 starts.
Aces were out on Sunday. AL Cy Young winner David Price also got rocked as the Rays lost to Cleveland by the same 13-0 score.
Lester (2-0) allowed five hits, all singles, in seven shutout innings.
"A lot of quality strikes," Farrell said. "He delivered the ball downhill. He carried his stuff through the full seven innings."
Lester walked none and struck out six, improving to 6-2 with a 2.13 ERA in his past nine starts at Rogers Centre.
"His performance was kind of overshadowed because we hit six home runs," Middlebrooks said. "He shut out a good hitting team. All his pitches were on and when that cutter is on, he's really dangerous."
Clayton Mortensen pitched the final two innings for Boston.
Blue Jays slugger Jose Bautista was held out of the starting lineup, the third straight game he's missed with a sore right ankle. The two-time major league home run leader twisted his ankle stepping on first base while beating out a double play in the eighth inning last Thursday.
NOTES: Red Sox DH David Ortiz (right heel) is set to play in extended spring training games starting Monday and could begin a rehab assignment with Triple-A Pawtucket as early as Thursday, manager John Farrell said. ... Boston SS Stephen Drew (concussion) will play two more games with Double-A Portland before rejoining the team in time for Wednesday's game against Baltimore. ... Lester had to jump out of the way of Edwin Encarnacion's shattered bat in the fourth. Encarnacion grounded to short on the play. ... Toronto claimed RHP Edgar Gonzalez off waivers from Houston and transferred RHP Dustin McGowan from the 15-day DL to the 60-day DL. ... The Red Sox open their home schedule at Fenway Park on Monday afternoon. RHP Clay Buchholz faces Baltimore LHP Wei-Yin Chen.