"Otherworldly hitting," New York manager Aaron Boone said of Guerrero. "One of the best hitters in the world."
The American League MVP runner-up homered off Cole in the first inning, had his hand accidentally spiked on a play at first base in the second and hammered a line-drive homer off Cole in the third to put Toronto up 3-0. He doubled off Cole in the sixth -- prompting the pitcher to make a show of tipping his cap to the 23-year-old -- then launched a 443-foot leadoff homer against Jonathan Loaisiga in the eighth for a 5-3 lead.
"Did you see his night?" Cole said in his postgame availability when asked about the tip of the cap. "If you had a cap, you'd tip it too."
It was the second three-homer game of Guerrero's career, matching a career high set last April 27 against the Washington Nationals.
The Blue Jays have taken two of three from the Yankees with the series finale Thursday. New York's new lineup has struggled offensively during this season-opening homestand, even drawing some boos from the Yankees faithful.
It seemed like Guerrero would have to leave in the second inning when his bare throwing hand was accidentally spiked by baserunner Aaron Hicks. Guerrero had to reach across his body for infielder Bo Bichette's throw and placed his right hand down behind the first base bag to balance. Hicks stomped on it running out an infield single.
Guerrero immediately began waving the hand around then walked toward Toronto's dugout as blood dripped onto his uniform and the turf.
In a show of toughness sure to satisfy hockey-obsessed fans in Toronto, Guerrero had a trainer tape up his wound and jogged back to first base a couple minutes later.
With a bloody stain on the right thigh of his pants, he batted in the top of the third and turned Cole's 98 mph fastball into a 427-foot, two-run homer and a 3-0 Blue Jays lead.
Toronto manager Charlie Montoyo said after the win that Guerrero simply didn't want to come out of the game and that, of course, the team didn't want that either. Montoyo gave credit to the Toronto training staff as well for preparing the first baseman to return.
"Besides Vladdy, the trainers were the MVPs tonight," Montoyo said.
Guerrero got two stitches after the game but said his hand felt fine, although he anticipated some soreness might set in Thursday.
"It's not that bad," he said.
Guerrero used his right hand for high-fives with base coaches Mark Budzinski and Luis Rivera as he rounded the bases then clapped his hands together emphatically before touching home plate.
Guerrero's first homer was nearly robbed in center by Hicks, who leaped above the wall and briefly had the ball in his glove. It fell out when Hicks hit the wall, bounced off something beyond the home run barrier and fell back into play. A replay review confirmed the ball went out.
"I wish it was against somebody else," New York outfielder Aaron Judge said, "so I could've watched it on TV and didn't see it live."
Guerrero has four homers in six games this season after leading the majors with 48 last season.
The Associated Press contributed to this report.