Cano, Swisher and Andruw Jones all cleared the walls off Santana in a four-run third inning, helping the Yankees breeze to their 50th all-time Subway Series victory, spanning 85 contests since Interleague Play began in 1997.
Santana may have captured the attention of all five boroughs with his no-hitter one week prior over the Cardinals, the first in Mets history, but it was Kuroda who kept a sellout crowd on the edge of its seats.
"Especially with what Santana did last week, you're thinking, 'Maybe this is going to happen here,'" Yankees manager Joe Girardi said. "We've seen a lot of special things happen at Yankee Stadium. It's unfortunate it didn't, but he still pitched a great game."
Kuroda faced the minimum into the sixth inning before Omar Quintanilla notched the only hit of the night against him, a double to left-center. Kuroda said he has never thrown a no-hitter, but he wasn't disappointed.
"I don't think it's an easy task," Kuroda said. "Rather than get a no-hitter, I just wanted to win, so I just focused on that."
Kuroda came out of the game after being hit on the left foot with a Daniel Murphy liner -- a ball that was caught by Alex Rodriguez on the fly for an out -- completing seven one-hit innings.
"He was filthy," the Mets' Jason Bay said. "I faced him a few times when he was with the Dodgers. He's always been, from what I've seen, pretty good. But that was by far the best I've ever seen him."
The Yankees have some concern about Kuroda's availability to make his next turn; X-rays revealed no fracture, only a contusion, but the hurler left the Stadium using crutches.
"I was pretty confident I was going to go out there in the eighth and ninth inning," Kuroda said through an interpreter, explaining that head athletic trainer Steve Donohue stopped him. "It was for the team. I'll be ready for my next start."
By that point, victory seemed a formality for the Yankees as Santana turned in a forgettable outing that saw him tie his career high in home runs allowed. Mets manager Terry Collins regretted his call to push Santana back two extra days after his heavy workload last time out.
"I know there were a lot of expectations and a lot of people waiting for tonight, but it just happened," Santana said. "It's done and I have to get ready for my next one."
Santana allowed six runs in five innings, hit hardest by Cano. Santana had allowed just two homers to left-handed batters in his last 27 starts before Cano got him twice with well-struck lasers in the second and third innings.
"Especially a guy like him, one of the best in the game, I would say you've got to be lucky to be successful," Cano said. "The guy threw a no-hitter his last start."
Swisher and Jones added roundtrippers to mark the first time the Yankees hit three consecutive homers since Aug. 28, 2011, against the Orioles, when the same three hitters hit the shots in the same order.
"Tonight was just kind of one of those magical nights," Swisher said. "It doesn't happen very often. It's something cool to be a part of."
Kuroda retired the first 10 batters he faced before Derek Jeter booted a Josh Thole grounder for an error, but Kuroda continued to face the minimum, inducing David Wright to hit into an inning-ending double play.
Though Kuroda had never had much success against the Mets before, going 1-5 with a 5.75 ERA in seven starts, he proved that didn't mean much in a 91-pitch effort that saw the veteran walk one and strike out seven.
"When we talked about Hiroki when we got him, that's what we expected," Girardi said. "This guy knows how to pitch, and that's what he did today."
The Yankees added three runs in the seventh off reliever Elvin Ramirez. Lucas Duda's ninth-inning RBI double off former Mets reliever Ryota Igarashi, making his Yankees debut, accounted for the Mets' only run.
The Yankees have won 11 of their last 15 games and moved a season-high seven games over .500 (32-25).
"Every series is big for us," Cano said. "All we're trying to do is go out there and win series."