The victory, propelled by a grand slam from Nicholas Castellanos, a career-best four hits by Niko Goodrum and seven strong innings by starting pitcher Jordan Zimmermann, ended an 11-game losing streak.
It was the Tigers' longest losing streak since Aug. 13-23, 2003. They have not lost 12 in a row since 1996.
"It's good to hear the music playing out there and guys smiling," Tigers manager Ron Gardenhire said.
The Tigers have a chance to escape the Rogers Centre with a split in the four-game series by winning the finale on Monday afternoon.
The Tigers will start right-hander Mike Fiers (5-4, 4.04 ERA) against Blue Jays left-hander Ryan Borucki (0-1, 3.00 ERA).
The Tigers had a team meeting before the game.
"It was just a casual talk," Gardenhire said. "It wasn't this rah-rah [speech]. ... I just let them talk and I just said to them, 'Tell me what we need to do.' Some guys spoke up and that's all I wanted to hear. We're playing hard. We've lost 11 in a row up to this point. These guys have been playing, man. They've been in every game. We've had a chance to win a bunch of these games."
The Tigers (37-48) were able to put together a five-run fifth inning with a rally that started with two outs against Toronto starter J.A. Happ, who was 6-0 in his previous eight starts. They added two runs in the sixth, also with a rally that began with two outs.
The losing streak was the longest by two games in the majors this season and the longest since the Los Angeles Dodgers lost 11 in a row last September.
"We've had our chances over the last 10 or 11 games," Zimmermann said. "It's just a matter of if we're going to cash in when we've got guys in scoring position. We were able to do that today."
The Blue Jays (39-44) are expected to trade Happ before the July 31 deadline. When he departed in the sixth inning, the Canada Day crowd gave him an ovation.
"I did notice, and I certainly appreciate that," Happ said. "Maybe it was appreciation for how the season has gone so far or whatever you might take from it, that's kind of what I took from it. That's a nice feeling, certainly nicer than potentially getting booed, not that I would expect that at all, either."
The Tigers face a pitcher who made his major-league debut Tuesday against the Astros in Houston in Borucki. He took the loss after allowing two runs, six hits and four walks in six innings.
Fiers pitched seven strong innings Wednesday against the Oakland Athletics, but took the loss despite allowing only one run on five hits and one walk while striking out five.
Fiers has faced the Blue Jays six times in his career, five as a starter, and is 1-3 with a 4.11 ERA. He made two starts against Toronto last season and was 0-1 with a 5.25 ERA. In two career starts at the Rogers Centre, Fiers is 0-2 with a 5.91 ERA.
The only disappointing news for the Tigers on Sunday came from a hamstring injury to center fielder Leonys Martin, who hobbled off the field after beating out an RBI bunt single in the fifth inning. It was at first announced as a cramp, but Gardenhire said the injury was severe enough to put him on the disabled list. Another player will be brought in for the game Monday.
The day was not a complete loss for the Blue Jays. In the ninth inning, center fielder Kevin Pillar made a spectacular leaping catch to rob Castellanos of what would have been his second homer of the day.
Gardenhire said even Castellanos appreciated Pillar's catch, although it cost him a homer.
"That was amazing," Gardenhire said. "That's a long run, to climb the wall like that and make that play, the timing, the whole package that just tells you how special an athlete he is."
The teams are 3-3 in the season series.