Pete Alonso celebrates after hitting a three-run home run in eighth inning of the Mets’ 4-2 win over the Brewers in Game 3 of their wild card series on Monday in Milwaukee. Morry Gash/Associated Press

MILWAUKEE — Pete Alonso hit a go-ahead, three-run homer off closer Devin Williams in the ninth inning and the New York Mets beat the Milwaukee Brewers 4-2 on Thursday night to win their NL wild card series.

With their latest thrilling comeback in the decisive Game 3 against Milwaukee, the Mets advanced in the playoffs for the first time since winning the 2015 National League pennant. They move on to a best-of-five Division Series beginning Saturday in Philadelphia against the NL East champion Phillies.

It will be the first postseason meeting between the longtime rivals.

New York went 6-7 against the Phillies during the regular season and finished six games behind them in the division standings.

The Brewers, making their sixth playoff appearance in the last seven years, still haven’t won a postseason series since reaching Game 7 of the NL Championship Series in 2018.

This series loss will be particularly painful.

Milwaukee appeared to have the victory in hand after Jake Bauers and Sal Frelick broke a scoreless tie by opening the seventh inning with back-to-back homers off José Buttó. Tobias Myers and three relievers had combined on a two-hit shutout through the first eight innings.

Twelve straight Mets had been retired when they opened the ninth against Williams, a two-time NL reliever of the year who had earned the save Wednesday in Milwaukee’s Game 2 victory.

But he wasn’t his normal self on this night.

Francisco Lindor opened the ninth by walking on a 3-2 pitch outside. After Mark Vientos struck out, Brandon Nimmo singled to put runners at the corners.

That brought up Alonso, who has 226 career homers in six seasons but hadn’t gone deep since Sept. 19.

After getting ahead 3-1 in the count, Alonso sent a 3-1 changeup over the wall in right field. He put his fingers to his mouth in a “chef’s kiss” gesture as he rounded first and gave the Mets the lead.

Williams remained in the game but never regained his footing. Jesse Winker was hit by a pitch with two outs, stole second and scored an insurance run on Starling Marte’s single to right. Winker, a former Brewer who was showered with boos throughout the series, screamed and slammed his helmet to the ground after sliding across the plate.

The ninth-inning comeback continued New York’s storybook season. The Mets were 22-33 in late May but played as well as anyone in baseball the rest of the regular season. They didn’t clinch a playoff berth until they scored all their runs in the final two innings of an 8-7 victory over Atlanta in the opening game of a doubleheader Monday, the day after the regular season was supposed to end.

Frelick led off the bottom of the ninth with a single, but Joey Ortiz struck out and Brice Turang hit into a double play to end the series.

Edwin Díaz pitched 1 2/3 innings of scoreless relief to earn the win. David Peterson, making his first relief appearance of the season, worked the ninth to pick up his first major league save.

The game started out as a pitchers’ duel between Myers and New York’s Jose Quintana. Myers pitched five shutout innings, while Quintana held the Brewers scoreless through six.