Quantrill pitched seven shutout innings and won his fifth straight decision, and Naylor hit a two-run home run as the surging Guardians won their season-high sixth straight.
''It's awesome,'' Naylor said of his and Quantrill's big games. ''This is where we kind of grew up playing baseball. We decided our paths here in Canada and we stuck with it, we grinded. It's tough being a Canadian coming up through baseball, but when you work hard, anything is possible.''
On Sitcom Night in Toronto, there was little for a big crowd of 41,677 to laugh at. Cleveland's Jose Ramirez hit a three-run home run, his 22nd, and finished with four RBIs as the Guardians roughed up Blue Jays right-hander Jose Berrios.
Toronto has lost three straight and six of eight.
Cleveland's streak has carried the Guardians to the top of the AL Central.
''I think that we're here to stay,'' Quantrill said. ''I don't think it's a fluke. We know how to win baseball games and we're kind of a complete baseball team.''
Quantrill, whose father Paul pitched for the Blue Jays, is from Port Hope, about 60 miles east of Toronto on the shores of Lake Ontario. Quantrill said he had 25 or 30 friends and family at the game, including his dad, as well as several former youth coaches and teammates.
''There were a lot of people I owe my career to at the game today,'' Quantrill said. ''It's fun to pitch well in front of those guys.''
Naylor is from Mississauga, the city immediately west of Toronto. He had around 100 people at the game, including three former teachers. Naylor stuck around on the field after the game, signing autographs for his entire party.
''I just wanted to show my gratitude and just thank everyone for being here for me,'' Naylor said.
Quantrill (9-5) allowed one hit, walked none and struck out seven. The Guardians have won each of Quantrill's last seven starts.
''He was phenomenal,'' Naylor said.
Eli Morgan gave up a two-out double in the eighth and Nick Sandlin pitched around a leadoff single in the ninth to complete the three-hitter.
Berrios (8-5) allowed eight runs and eight hits in four innings, losing for the first time in 12 home starts in 2022.
Quantrill retired the first 10 batters in order before Blue Jays designated hitter Vladimir Guerrero Jr. doubled in the fourth, extending his career-best hitting streak to 21 games. Quantrill finished his outing by setting down the next 11 in a row.
''I thought he was so good tonight,'' Cleveland manager Terry Francona said. ''It's nice when you're in the middle of August and a guy looks like his last pitch was as good as his first.''
Berrios hit Austin Hedges with one out in the third, Will Benson singled and Steven Kwan loaded the bases with a bunt single that rolled 45 feet along the third base line before bumping into the bag.
Amed Rosario hit a two-run single, Ramirez followed with a sacrifice fly and Naylor homered to left, his 15th, to cap a five-run inning.
Berrios walked two batters in the fourth before Ramirez connected on a changeup that was well below the strike zone.
''He stayed through it so nice,'' Francona said of Ramirez's homer.
It's the second time this season that Berrios has allowed eight earned runs. He also did it in a June 26 loss at Milwaukee. He allowed a career-worst nine earned runs against Atlanta on Aug. 6, 2019, while pitching for Minnesota.
Berrios went 3-0 with a 3.00 ERA in six July starts, but is 0-1 with a 15.25 ERA through two starts this month.
''I don't feel too happy right now with my last two starts,'' Berrios said.
Berrios has a 5.61 ERA through 23 starts, worst among qualified MLB pitchers.
Ramirez went 3 for 3 with a walk. He was replaced by pinch runner Tyler Freeman after an infield single in the eighth. Ramirez singled to right in the first against a four-man outfield.
Blue Jays: OF George Springer (right elbow) has resumed throwing and has been hitting off a tee, interim manager John Schneider said. Springer went on the 10-day IL Aug. 5. . RHP Ross Stripling (right hip) pitched five shutout innings Friday in his first rehab start for Triple-A Buffalo. Stripling, who went on the 15-day IL on July 31, is expected to rejoin Toronto's rotation next week.
Guardians: Cleveland put unvaccinated RHP James Karinchak on the restricted list and selected RHP Peyton Battenfield from Triple-A Columbus.
Blue Jays: RHP Matt Peacock cleared waivers and was assigned to Triple-A Buffalo.
Kwan made a sensational diving catch to retire Toronto's Lourdes Gurriel Jr. in the bottom of the first, sliding along the warning track after hauling in Gurriel's deep line drive.
''Our outfield has been fantastic this year,'' a grateful Quantrill said. ''It's a huge weight off the pitcher's shoulders.''
SWINGING A NEW STICK
Toronto Maple Leafs star Mitch Marner took some swings in the cage before batting practice.
Cleveland RHP Triston McKenzie (8-8, 3.16) starts Saturday against Blue Jays RHP Mitch White (1-3, 3.86). McKenzie pitched eight shutout innings in a 1-0 victory over AL West leaders Houston in his previous start.
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