NEW YORK — Their rotation ravaged, the Mets handed the ball to a rookie for his first major league start.

Their late-inning relievers run down, they allowed a 33-year-old left-handed specialist to face the big leagues’ No. 2 home-run hitter with two outs in the ninth.

With veterans tired after an extra-inning win, backups filled many of the starting spots.

In yet another surprising September turn, Gabriel Ynoa struck out eight over 4 2/3 innings, Jerry Blevins fanned Brian Dozier to complete a four-out save and New York completed a three-game sweep of the woeful Minnesota Twins with a 3-2 victory Sunday.

Michael Conforto drove in two runs with a first-inning, opposite-field single to left, his first multi-RBI game since June 8. T.J. Rivera, a Bronx-born 27-year-old rookie, added a third-inning homer off Kyle Gibson (6-10).

“This is our season in a nutshell,” Blevins said.

A season-high 11 games over .500, the Mets won for the 11th time in 14 games despite benching Jose Reyes, Asdrubal Cabrera, James Loney, Curtis Granderson and Jay Bruce from the starting lineup after Saturday’s late-night win, powered by Granderson’s home runs in the 11th and 12th innings.

New York opened a one-game lead over San Francisco for the NL wild-card lead, with St. Louis another game back. The Mets’ 13 remaining games are against teams with losing records: Atlanta, Philadelphia and Miami.

“You’ve got to have guys that when they get the opportunity come through,” Mets manager Terry Collins said.

So under-the-radar that he is able to ride in a scooter from his Manhattan apartment to the subway, then scoot the short distance from the subway to the players’ entrance at Citi Field, Blevins wants to make up for last year. He was limited to seven games after his left arm was broken by a line drive in April, then fractured again when he slipped off a curb in August. He lost a chance to pitch against left-handers in October.

“The Royals have a ton of them, so that was heartbreaking for me as a competitor,” he said.

With closer Jeurys Familia and set-up man Addison Reed unavailable, Blevins retired pinch-hitter Eduardo Escobar on a popup to strand Robbie Grossman at third in the eighth inning.

He struck out John Ryan Murphy starting the ninth, then got pinch-hitter Joe Mauer to pop out. After a mound visit by pitching coach Dan Warthen, Blevins threw a pair of called strikes to Dozier and got him to swing over a curveball in the dirt.

“He’s done it 41 times. He wanted to tie the ballgame up,” Blevins said. “So you try to give him something that looks like a strike and make him chase.”

New York’s sixth pitcher, Blevins got his fourth career save and second this year. Dozier had extended his hitting streak to 22 games with a fifth-inning single that chased Ynoa.

Ynoa started in place of 2014 NL Rookie of the Year Jacob deGrom, likely out for the rest of the year because of an injury to the ulnar nerve in his right elbow that probably will require surgery. Ynoa entered with a 15.19 ERA in six relief appearances and became the Mets 11th starter this season.

He allowed four hits, one walk and Murphy’s sacrifice fly in the second.

“I was informed yesterday and I prepared myself mentally on the fly,” he said through a translator.

After a strong start as a rookie last year, Conforto was demoted to Triple-A twice this season and entered Sunday hitting .214. Rivera spent six seasons in the minors before making his debut Aug. 10.

“You visualize this moment all your life,” Rivera said.

Erik Goeddel (2-1) struck out Kennys Vargas to strand the bases loaded in the fifth, and Vargas cut the lead to one when he homered in the eighth against Fernando Salas, a drive off the Wise billboard above the bullpens. Blevins then held on.

“We’re in a position where if we play well, play the way we know we can the rest of the way,” Conforto said, “we’ll be playing playoff baseball.”

GIDDY-UP

After riding a horse at spring training one day, Cespedes is to visit Cespedes, a thoroughbred named after him, at Belmont Park on Tuesday.

LATE SHOW

Granderson joined Philadelphia’s John Mayberry Jr. (June 4, 2013) and St. Louis’ Matt Adams (Sept. 4, 2013) as the only players in the last 25 years to go deep twice in extra innings in the same game, according to the Elias Sports Bureau.

TRAINER’S ROOM

Lucas Duda went 0 for 2 in his return from a stress fracture in his lower back, an injury that had sidelined him since May 20. … Juan Lagares, coming off left thumb surgery, played center field in the ninth, his first appearance since July 28. … LF Yoenis Cespedes left after six innings because of a nausea and dizziness. … Collins wanted to play Wilmer Flores (wrist), but the infielder was unable to swing a bat. Flores has not played since Sept. 10. … Collins said LHP Steve Matz (left shoulder tightness) could take this rotation turn the next time it comes up, which would be his first appearance since Aug. 14.

UP NEXT

Mets: RHP Noah Syndergaard (13-8) starts on five days’ rest in Monday’s series opener against Atlanta and RHP Aaron Blair (0-6). Syndergaard has a 1.36 ERA in his last six starts.