NEW YORK -- It was the third inning and Jordan Montgomery stood near the top of the Citi Field mound on Tuesday, seemingly confused by the unwelcome visitor approaching. Greeting manager Aaron Boone, who was extending his right hand to claim the baseball, the left-hander mouthed: “Why?”

A brief explanation followed; Boone patted his hurler’s chest as something of an apology, though the five runs already on the scoreboard told the tale. Montgomery permitted early homers to Starling Marte and Eduardo Escobar and the Yankees couldn’t catch up, dropping the Subway Series opener to the Mets, 6-3.

“I wanted to be out there, but I sucked,” Montgomery said. “Obviously, I needed to be pulled. But I was ready to throw as many pitches as necessary.”

Seventy-one had been enough, in Boone’s view. Montgomery’s stumbles flushed a lead, as Aaron Judge and Anthony Rizzo slugged back-to-back homers in the first inning off Taijuan Walker, including Judge’s Major League-leading 38th of the year.

“That’s the thing about Monty; he always wants the ball,” Boone said. “Whether it’s going great or a night like tonight where he’s struggling, he wants to compete. But at that point, the kind of at-bats they were having against him, I just felt like that was the time.”

Montgomery’s shortest outing of the season dropped his record to 0-3 with an 8.40 ERA in four career starts against the Mets. The Yanks still own baseball’s best record (66-32), but July has not been kind, as they have lost 11 of 21 contests.

“It wasn’t going to be perfect all year,” Boone said.

Despite the early deficit, the Yankees did not roll over in this showdown of first-place clubs, the first time both participants entered a Subway Series occupying sole possession of the top spots in their respective divisions since Interleague Play began in 1997.

“Right now, they're the best team in the American League, and this is a really good test for us,” the Mets’ Pete Alonso said. “We want to end up beating a team like that.”

Alonso got his wish, partly because the visitors missed opportunities aplenty -- Isiah Kiner-Falefa stewed at his locker after the game, lamenting a second-inning pickoff that short-circuited a rally, while complimenting Walker’s pickoff as “the fastest move I’ve seen.”

“It’s tough, but we’ve been trying to be aggressive all year,” Kiner-Falefa said. “That’s something that they wanted me to bring when I got traded here. I’m always going to be as aggressive as I can. I’ve just got to clean some things up and do a better job of knowing how quick [the pitcher] is.”

The Yanks’ bullpen combined for 5 2/3 innings of one-run relief, including an encouraging 1-2-3 sixth from Aroldis Chapman, but the bats struggled to break through.

A bases-loaded, one-out chance in the fourth yielded only one run, pushed home by a DJ LeMahieu groundout, and Rizzo was cut down on the back end of a double steal in the seventh.

Kiner-Falefa has been swinging a hot bat, extending his hitting streak to 13 games -- the longest by a Yankee this season. But with the Bombers’ chances dwindling, Boone decided to push the power button in the eighth, sending up Joey Gallo to pinch-hit for Kiner-Falefa as the potential tying run.

“In that situation, you need two runs,” Kiner-Falefa said. “Joey’s been one of the best power hitters in the game the last couple of years, and I’ve got zero [homers], so there’s nothing that I can say. Give him an opportunity to tie the game.”

In that spot, Boone was willing to look past Gallo’s sub-.200 batting average and more than a calendar year of struggles; maybe one big swing would change the narrative, at least for a night.

But the Mets countered with flame-throwing closer Edwin Díaz -- 27 of Diaz’s last 36 outs have come via strikeout, a collection that would soon include Gallo.

“Just about every inning, we had opportunities and weren’t able to punch through,” Boone said. “That’s kind of the difference when you’re playing some of these close games. We were pretty consistently pushing through and winning those games, [and] we’ve lost a few of those over this stretch. We know we can be a little bit better.”