NEW YORK — Clayton Kershaw finally came through in October, just in time to save the Los Angeles Dodgers from another early exit.

Pitching on short rest with the season on the line, Kershaw shut down the New York Mets for seven innings and Justin Turner delivered a key hit against his former team that sent the Dodgers to a 3-1 victory Tuesday night and forced the NL Division Series to a deciding Game 5.

The series shifts back to Los Angeles on Thursday night, with fellow Dodgers ace Zack Greinke scheduled to start against Jacob deGrom. The winner hosts the wild-card Chicago Cubs in the NL Championship Series opener Saturday.

With Chase Utley on the bench again, the Dodgers handed hometown Mets rookie Steven Matz his first loss in the major leagues.

Kershaw’s one-out single led to a three-run third. Adrian Gonzalez looped an RBI single and Turner added a two-run double, providing enough support for the lefty ace.

The reigning NL MVP and three-time Cy Young Award winner snapped a five-start losing streak in the playoffs — the longest in Dodgers history.

After dropping the series opener 3-1 to deGrom, Kershaw was 1-6 with a 4.99 ERA in 12 career postseason games, including nine starts. He had lost elimination games each of the past two years, once on three days’ rest.

But this time, Kershaw was just as dominant as he normally is during the regular season.

Kershaw struck out eight, walked one and yielded only three hits, quieting another revved-up crowd at Citi Field as the night wore on. Daniel Murphy hit his second solo homer off Kershaw in the series, both coming in the fourth inning.

Kenley Jansen got four outs for his second save. With two runners on in the eighth and the count full, he retired Murphy on a fly to right. The right-hander then worked a 1-2-3 ninth as the Dodgers ended a seven-game losing streak in road playoff games.

The 24-year-old Matz was pitching in a big league game for the first time in 19 days after a balky back sidelined him late in the season. Still, he looked sharp early and snapped off several effective curveballs.

That same pitch caused him trouble, too.

Kershaw singled to left-center on a 2-2 curve in the third for the first hit of the game. With two outs, Howie Kendrick grounded a single up the middle and Gonzalez dumped an RBI single into center.

Turner then lined a 2-0 curve into the left-field corner to make it 3-0, tormenting his former team yet again. Let go by the Mets after the 2013 season — they declined to offer him arbitration — he is 7 for 15 (.467) in the series with four doubles and three RBIs.

His next time up, Turner was intentionally walked.

Matz grew up a Mets fan on Long Island, about 50 miles from Citi Field, and his family attended the game. He went 4-0 with a 2.27 ERA in six major league starts this season, but the team saw enough to pitch him in the playoffs — in part because Matz threw gems to help clinch championships at Class A in 2013 and Double-A last year.

One of Matz’s best outings came at Dodger Stadium, where he tossed six shutout innings of two-hit ball with eight strikeouts July 5 to win his second major league start.

This time, the left-hander was pulled for a pinch hitter in the fifth after giving up three runs and six hits.

Dodgers catcher A.J. Ellis extended his postseason hitting streak to 12 games, setting a franchise record. He has hit safely in 15 of 16 career playoff games.

TRAINER’S ROOM

Dodgers: Slumping C Yasmani Grandal (left shoulder) was available off the bench after he “kind of pinched something” in his last at-bat Monday night, manager Don Mattingly said. Ellis was scheduled to catch Kershaw anyway, with a lefty on the mound for the Mets.

Mets: A starter during the regular season, 42-year-old Bartolo Colon replaced Matz and tossed two shutout innings after throwing 26 pitches in relief Monday night.

UP NEXT

Dodgers: Greinke allowed a pair of solo homers during a 5-2 victory in Game 2. He went seven innings and struck out eight without a walk. The right-hander is 3-2 with a 3.48 ERA in eight postseason starts. He was 19-3 with a 1.66 ERA this season, the lowest in the majors since Atlanta ace Greg Maddux posted a 1.63 mark in 1995. Los Angeles went 43-22 this season in starts by Kershaw and Greinke, and the duo combined to go 35-10 with a 1.90 ERA.

Mets: Making his postseason debut, deGrom beat Kershaw 3-1 in the series opener at Dodger Stadium. Last season’s NL Rookie of the Year pitched seven scoreless innings and struck out 13, matching Tom Seaver’s franchise record for a postseason game.

Los Angeles Dodgers pitcher Clayton Kershaw (22) delivers against the New York Mets during the first inning of baseball’s Game 4 of the National League Division Series, Tuesday, Oct. 13, 2015, in New York. (AP Photo/Kathy Willens)