NEW YORK -- As he stood near the third base coach's box in the ninth inning Wednesday night, Roberto Kelly implored the San Francisco Giants to score just one run to support yet another singular postseason performance by Madison Bumgarner.

With the biggest swing of his life, Conor Gillaspie provided everything Kelly wanted and more, sending baseball's even-year dynasty into a clash with the team looking to end the longest title drought in sports.

Gillaspie's ninth-inning, three-run homer snapped a scoreless tie Wednesday night, and Bumgarner threw his third career postseason shutout as the Giants beat the New York Mets 3-0 in the National League wild-card game at Citi Field.

Next up for the Giants, who won the World Series in 2010, 2012 and 2014: the Chicago Cubs, who haven't won it all since 1908. The Cubs will host Game 1 of the best-of-five NL Division Series on Friday night.

"Bum just did his thing," Giants manager Bruce Bochy said. "We won the game because of him. It's great to get that big hit, but it starts with the pitcher, and that's what Bum gave us."

Bumgarner allowed four hits and two walks (one intentional) while striking out six. He threw 119 pitches (78 for strikes). The Mets didn't get a runner beyond second base against Bumgarner, who allowed just three runners to get into scoring position.

The shutout was the second in a wild-card game in as many appearances for Bumgarner, who also four-hit the Pittsburgh Pirates in 2014. He has given up one run in his past 30 postseason innings dating back to the start of the 2014 World Series.

"I've been blessed with a lot of opportunities," Bumgarner said. "But I've played this game enough to know that anything can happen, especially this time of year."

In addition, Bumgarner has thrown 23 consecutive scoreless innings in his three appearances in winner-take-all postseason games -- the wild-card game shutouts plus his five-inning save in Game 7 of the 2014 World Series against the Kansas City Royals.

"It's pretty special," Giants right fielder Hunter Pence said. "You can't put words to describe how remarkable his performances are, in the biggest moments, how he rises to the occasion. It's special to be his teammate."

It appeared as if Bumgarner might not factor into the decision when the Giants began to rally against Mets right-hander Jeurys Familia in the ninth. Brandon Crawford hit a leadoff double and Joe Panik worked a one-out walk to bring up Gillaspie, who was in the lineup because Eduardo Nunez has a hamstring injury.

With Jarrett Parker on deck to hit for Bumgarner, Gillaspie homered well beyond the right field fence. The 29-year-old Gillaspie, who was a first-round pick of the Giants in 2008 but bounced to the Chicago White Sox and Los Angeles Angels before returning to San Francisco in February, nearly sprinted around the bases.

"I lost it when that ball went over the fence," Gillaspie said. "This is something you dream about your whole life, to be able to do something like that in a postseason game."

Kelly was so excited, he was two-thirds of the way down the third base line when he exchanged high-fives with Gillaspie.

"Man, I was so excited to get a run across the plate -- I knew all we needed was one the way Bum was pitching," Kelly said. "Yeah, I was excited."

Bumgarner flied out to the track in left field before setting the Mets down 1-2-3 in the ninth to cap a pitchers' duel that lived up to expectations and then some.

Mets ace right-hander Noah Syndergaard carried a no-hitter into the sixth inning and ended up allowing just two hits and four walks while striking out 10 over seven scoreless innings. He allowed just two Giants to get into scoring position and no one to reach third base.

"He rose to the occasion," Mets manager Terry Collins said. "That's why I think he's going to be very special, because you can't be a lot better when you're challenged in these situations. He did a great job."

The Mets, who were under .500 as recently as Aug. 21 and fielded a lineup Wednesday featuring just three Opening Day starters, were eliminated from the postseason at home for the second straight season. The Royals clinched the World Series with a Game 5 win at Citi Field last Nov. 1.

"They're down," Collins said of his players. "but they shouldn't be, because there's only a few teams that could have come back under the circumstances we came back on. I'm really proud of them."

NOTES: The most notable absences from the 25-man rosters were Mets 1B Lucas Duda and Giants 3B Eduardo Nunez. Mets manager Terry Collins said he preferred switch hitter Ty Kelly over the left-handed-hitting Duda, who batted .217 in eight games after returning Sept. 18 following a four-month stint on the disabled list caused by a stress fracture in his lower back. Giants manager Bruce Bochy said Nunez, who strained his right hamstring Sept. 25, wasn't able to sprint at 100 percent. ... The home team fell to 3-7 in wild-card games, which began in 2012.