Shane Victorino hit the go-ahead two-run single in the top of the 11th inning, as Boston outlasted Toronto, 4-2, in the opener of a three-game set.
Jacoby Ellsbury and Dustin Pedroia knocked in a run each for the Red Sox, who had dropped three of four in Kansas City prior to arriving in Canada.
Koji Uehara (3-0) tossed the final 1 1/3 innings of scoreless relief for the win.
J.P. Arencibia homered and drove in both runs for the Blue Jays, who slid to their fifth loss in six games.
Aaron Loup (4-5) was charged with the deciding hit while recording two outs in the 11th.
Against Loup, the seventh of eight Toronto hurlers, Jarrod Saltalamacchia walked with one out and Will Middlebrooks singled, but the latter was erased on an Ellsbury fielder's choice grounder that left runners on the corners. Ellsbury stole second to put two runners in scoring position, and Victorino then laced a line single to center for a 4-2 contest.
Uehara, who fanned Jose Reyes to end the bottom of the 10th, turned in a placid final half frame to lock up the victory.
The Jays cracked the scoreboard in the fifth. Brett Lawrie socked a one-out double to right, moved up on a Maicer Izturis flyout and scored when Arencibia laced a single to left.
Boston loaded the bases with one out in the sixth and failed to score, then dodged a bullet in the last of the inning when Reyes worked a leadoff walk and was eventually thrown out at home trying to score on an Edwin Encarnacion single.
Middlebrooks doubled in the seventh and came in when Ellsbury followed with a base hit. Ellsbury swiped second, went to third on a Victorino groundout and came in on a Pedroia single for a 2-1 game.
Arencibia kicked off the home half with a blast to left, but the Jays couldn't score in the ninth despite runners on first and second.
Boston starter Ryan Dempster worked seven innings, allowing one run and four hits ... The Red Sox improved to 9-4 in their last 13 games at Rogers Centre ... Pedroia has hit safely in his last 15 games against Toronto, the longest current streak by any active player against Blue Jays ... Prior to the game, the Red Sox announced that catcher David Ross was sent on a rehab assignment to Triple-A Pawtucket ... The Jays announced Tuesday that starting pitcher Josh Johnson is headed back to the disabled list (right forearm strain), and will recall right-hander Thad Weber from Triple-A Buffalo ... Jays starter Todd Redmond, summoned from the minors after the club placed pitcher J.A. Happ on the bereavement list, lasted just 5 1/3 innings but held the Sox scoreless on three hits.