There wasn't much boasting -- or clucking? -- from the visitors, but the Yankees hadn't appreciated the fowl taunts from the Mets' Frank Francisco, who added injury to insult as he ended the weekend on the disabled list with a left oblique strain.
"With all the talk coming into this, it's pretty good for us," Swisher said. "I feel like we wanted to go out there and win, with the little added something."
Cano atoned for an earlier error by crushing his 16th homer off Batista in the eighth, nearly depositing it into the Home Run Apple in center field.
Perpetually a club that lives and dies with the long ball without apology, the Yankees hit seven homers in the weekend series and appreciated Citi Field's new and friendlier dimensions.
"I never had it in my mind that I wanted to hit it out or anything like that," Cano said. "It was nice here to get a win. You want to hit homers, but you want to hit them in a situation like that, where you help the team get a win."
The Bombers' victory came on a night in which they were able to rough up Dickey for five runs in six innings, but CC Sabathia accepted a no-decision as wildness and defense let him down in his shortest start of the year.
Boone Logan picked up the win with four outs, while Rafael Soriano locked down the ninth inning for his 15th save in 16 chances.
Sabathia's lead was erased by three unearned runs in the sixth inning, as Cano's error on a bad-hop grounder opened the door for trouble.
"I just didn't make two-strike pitches," Sabathia said. "You have to give them a lot of credit. Still, I feel like I gave up a lot of hits with two strikes and they ended up coming back to get me."
Andres Torres made Sabathia pay for a free pass to Vinny Rottino, slicing a two-run single under Mark Teixeira's glove at first base that ended Sabathia's night after 5 2/3 innings. Teixeira said he'd been screened by Rottino, preventing him from making the play.
"That happens once or twice a year," Teixeira said. "It's just a weird play when I'm trying to field the ball -- the runner is right in front of me. It's always going to score a run; it stinks, but there's really not much you can do there."
Ruben Tejada greeted Cory Wade with a game-tying single to left field, as Sabathia wrapped up permitting five runs (one earned) on nine hits, walking two and striking out three.
"[The Mets are] just pesky, just shortening up and making contact," Sabathia said. "I didn't make good enough pitches with two strikes to get these guys out, and they extended innings and made me throw a lot of pitches."
Early on, it looked as if the Yankees might regret missing a prime run-scoring chance when Teixeira was held at third base in the second inning, only to be stranded there by the next two batters.
But the Yankees shattered Dickey's string of consecutive innings without an earned run at 44 2/3 in the fourth, as Teixeira lifted a sacrifice fly and Swisher crushed the three-run homer, his 11th.
"I just tried to look for something up in the zone and just got lucky on that," Swisher said, "because I've never hit a ball like that off a knuckleballer, I know that."
Dickey said that he didn't have a great knuckler working for him on Sunday, but he couldn't be intimidated by the Bombers' big-swinging lineup.
"They have the capability of beating you on one swing," Dickey said. "I was going to live and die with my girl. She's been nice so far, and that's just the way of it."
Teixeira's fifth-inning fielder's choice drove in the fifth and final run against Dickey, marking the first time since May 17 that the right-hander did not complete at least seven innings.
"When you throw two straight one-hitters, you're doing everything right," Teixeira said. "He might have been off a little bit."
Generally speaking, the Yankees are the team that tries to downplay the importance of the Subway Series, taking a corporate stance and discounting the fun as just three more games on the schedule.
But after getting the last word in the silly "chicken" back-and-forth, as well as yet another series victory, they might have to reconsider their stance on the Interleague destination.
"Rivalry series are awesome," Swisher said. "To get that fire and that energy back -- this ballpark was rocking. To be part of that, take two out of three, five out of six on the year -- it's not too shabby."