The Blue Jays (58-90) won the series opener 6-5 Friday night when Bo Bichette led off the bottom of the 12th inning with his 11th home run of the season.
"Against the best team in baseball, it's a great moment," Blue Jays manager Charlie Montoyo told reporters after the game.
The Blue Jays are 6-8 against the Yankees this season.
The Yankees (97-52) have been working overtime the past two days, sweeping a doubleheader from the Tigers in Detroit on Thursday before going extra innings on Friday in Toronto.
Paxton has won a career-best eight consecutive starts. His 13 wins for the season so far are also a career best.
He threw a no-hitter against the Blue Jays as a member of the Seattle Mariners last season.
Paxton is 3-3 with a 5.44 ERA in eight career starts against the Blue Jays and is 3-1 with a 4.30 ERA in five career starts in Toronto. He is 0-0, 9.00, in two starts this season against the Blue Jays.
Waguespack has faced the Yankees once, allowing three runs, three hits and three walks with two strikeouts in 3 2/3 relief innings on Aug. 10. He did not get a decision in the game.
Montoyo said that the win Friday was "bittersweet" because left-handed reliever Tim Mayza had to leave the game in the 10th inning. After allowing a walk on a pitch that went well behind batter Didi Gregorius, Mayza fell to his knees and clutched his elbow in pain. The team said he was to undergo an MRI exam Friday night.
The Blue Jays overcame another poor night defensively in the outfield, with Randal Grichuk's throwing error helping the first of five Yankees fifth-inning runs to score.
"We have to keep talking about it and keep working," Montoyo said.
He also used the game to send a message. He took Rowdy Tellez out of the game after the first baseman failed to run hard on a groundout in the fifth.
As for the Yankees, they have been dealing with injuries all season. On Thursday, pitcher J.A. Happ (biceps tendinitis) and sluggers Edwin Encarnacion (oblique) and Gary Sanchez (groin) joined the team's lengthy list of ailing players.
Yankees manager Aaron Boone declined to be specific about when Sanchez and Encarnacion might return.
"I don't want to start saying 10 days, two weeks, three weeks, all these things, because we're now in the early stages," Boone told reporters. "I would say, based on the information given to me, I have some optimism."
Sanchez has already missed 2 1/2 weeks with a previous groin injury this season.
"Hopefully we'll get him back by the end of the season, but obviously these next few days, how he responds and everything, we'll be able to determine the factor," Boone said.
Encarnacion has an internal oblique strain that is considered mild, so there is optimism about his situation.
Boone said that Happ is doing "pretty good" after receiving a cortisone injection. Happ is tentatively slated to start Thursday against the Los Angeles Angels.
The Yankees are 5-3 on their 10-game road trip that ends Sunday in Toronto.
--Field Level Media