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.

"Definitely happy to be going back home," Kershaw said. "They like us a little better there."

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 blooped 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.

"I'm actually really happy for him. I mean, this kid is tremendous. Everything that you're supposed to be, he is," Dodgers manager Don Mattingly said. "This guy's an animal, the way he works, represents us, the game of baseball, himself. I mean, he's really a credit to the game, and so you're really happy for him to be able to do that tonight."

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 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.

"There's no curse or anything," he said. "Just got to get through the seventh."

He 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.

"I feel confident with Zack going in Game 5 back home," Kershaw said. "I really wanted to win tonight, definitely. For a lot of reasons, but obviously most important was just to give Zack a chance."

Kershaw improved to 1-1 with a 1.89 ERA in a trio of playoff starts on three days' rest. He has 23 strikeouts in 19 innings during those games.

With a $290 million payroll that's $66 million higher than any other team, the Dodgers are seeking their first pennant since winning the 1988 World Series. They've captured three straight NL West titles but won only one playoff series during that span — in part because Kershaw got little run support in four consecutive postseason losses to St. Louis.

But after Los Angeles allowed 13 runs to the Mets in Game 3, a Dodgers postseason record, Kershaw restored order when his team absolutely needed it.

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 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.

"Honestly, I never thought he'd be this good of a hitter. He's one of the best hitters in the game," Kershaw said. "We thought he'd be a great utility player, and he's turned out to be our 3-, 4-hole hitter and our starting third baseman. So can't say enough about him."

His next time up, Turner was intentionally walked.

"He's changed his batting style a little bit, but he's a good baseball player. He always has been. He did a great job while he was here. We root for him. We all cheered for him. We like him," Mets manager Terry Collins said. "So we're happy for him. He's got an opportunity to play every day in L.A. and he's making the most of it."

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.

"The one pitch I know he wants back is the pitch to Kershaw," Collins said. "We've got all the confidence in the world that if we get to the next round, he's going to be a part of that rotation."

PLAYOFF PERFORMER

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.

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 last Friday at Dodger Stadium, deGrom pitched seven scoreless innings. Last season's NL Rookie of the Year struck out 13, matching Tom Seaver's franchise record for a postseason game.