Vernon Wells' two-run homer in the sixth was the only hit allowed by Vazquez (5-5).
"This is the guy that we thought we were getting," New York manager Joe Girardi said.
Vazquez walked four and struck out a season-high nine to win consecutive starts for the first time this year.
"The last couple of starts I've been feeling much better with my command and what my pitches are doing," he said. "I feel good that I could do it against an offense like the Blue Jays."
Girardi said Vazquez's changeup was the best it's been all season, and catcher Francisco Cervelli said that was the key to keeping Toronto's bats in check.
"They always take a big swing and hit a lot of homers so we just tried to change the rhythm a little bit," Cervelli said. "Offspeed is, I think, the best way."
New York's power-packed lineup managed just three runs in the first 30 innings of the series before scoring four times in the eighth.
The comeback spoiled a fine outing by Blue Jays right-hander Brandon Morrow, who left to a standing ovation after hitting Cervelli in the shoulder with a pitch to begin the eighth.
"Sometimes I think I should get thrown out in the first," Girardi said.
Girardi, who wasn't wearing his cap when he came out, kicked the dirt on either side of home plate and held his fingers apart in front of Dreckman's face before leaving the field.
"I thought the strike zone at times was generous, and I didn't think Swisher had swung," Girardi said. "I threw my hat when he called it and I didn't go back to get it."
Rodriguez struck out but Cano lined a two-run single to left.
Wells hit a two-run shot on an 0-2 slider with two outs in the sixth. His 15th homer extended his hitting streak to 14 games.
Bench coach Tony Pena, filling in for Girardi, came out of the dugout and motioned to the bullpen with his left hand -- but right-hander Mariano Rivera came jogging in from the bullpen. After Blue Jays manager Cito Gaston spoke with the umpires, they huddled and concluded that lefty Damaso Marte had been called for instead.
"I'm going to let Tony explain that to you," Girardi said. "Whatever it is, it worked."
Rivera walked back to the right-field bullpen, crossing paths with Marte on the way, and watched as Marte struck out Adam Lind to end the inning.
"I don't know what happened but I know that I was ready," Rivera said. "All of a sudden they sent me back."
Pena said he decided to go with Marte on his way to the mound.
"We discussed it in the dugout but when I walked out of the dugout I changed my mind and said, 'I'm going to use Marte," Pena said.
Rivera picked up the phone when he got back to the bullpen, looking for an explanation.
"I was trying to call somebody, but the guy hung up," he joked.
Rivera returned in the bottom of the ninth and closed it out for his 13th save in 14 chances.
Ramiro Pena came on to play third base in the ninth because Rodriguez was complaining of a sore right groin.
"It's fine now," Rodriguez said. "I'll be ready to go on Tuesday."
Pena was immediately tested when a grounder from Wells took a bad hop, but he recovered to make the play.
New York improved to 1-18 when trailing after seven innings. ... Teixeira, who was 0 for 6 with five strikeouts in Saturday's 14-inning loss, went 0 for 4 with an intentional walk, dropping his average to .211. ... Girardi said Jorge Posada (foot), limited to a DH role since coming off the disabled list last week, could resume catching drills during a series in Baltimore that begins Tuesday. ... Toronto 3B Edwin Encarnacion (sore legs) did not play. ... Blue Jays INF John McDonald has been away from the team all weekend to be with his father, who is ill.