NEW YORK -- The mood remained upbeat in the New York Mets dugout for the first few innings Sunday afternoon despite a scoreboard that painted anything but a rosy picture.

Down in the bullpen, right-handed pitcher Jeurys Familia had an even more optimistic outlook.

"One of the girls in the kitchen just told me Familia was in there to get some water in the fifth inning and said 'I don't care what the score is. We are going to win'" Mets manager Terry Collins said Sunday afternoon. "That's the confidence in the room."

It proved warranted Sunday, when centerfielder Juan Lagares' three-run sixth-inning homer capped a stunning comeback by the Mets, who went on to beat the Atlanta Braves, 10-8, at Citi Field.

The Braves jumped out to leads of 5-1 and 8-3 against Mets right-hander Dillon Gee, but New York stormed back against Atlanta's starter, right-hander Mike Foltynewicz, as well as right-hander Brandon Cunniff and left-hander Luis Avilan.

"I just think everybody stayed positive," Mets left fielder Darrell Ceciliani said. "Everybody was upbeat on the bench. It was just a good feeling. Not going down without a fight was kind of the mentality."

The Mets, who scored a run in the first when right fielder Curtis Granderson raced home on a wild pitch and two more in the third on a two-run single by shortstop Wilmer Flores, really began to chip away when Ceciliani and second baseman Dilson Herrera hit solo homers in the fourth.

After first baseman Lucas Duda chased Foltynewicz with a one-out single in the fifth, catcher Travis d'Arnaud greeted Cunniff with a two-run homer to pull the Mets within 8-7.

"With Travis' home run, I said 'We've got a shot here'", Collins said. "The guys just kept talking about pushing, pushing, pushing. What we had to worry about was our bullpen because we were out of pitching."

But left-hander Sean Gilmartin (1-0) threw a hitless fifth and sixth to begin quieting the Braves. Gilmartin and right-handers Bobby Parnell, Hansel Robles and Familia combined to allow two hits over the final five innings, during which Atlanta didn't get a baserunner beyond first base.

"They came in and they closed the door," d'Arnaud said. "They kept putting up zeroes on the board. They picked us up when we needed them."

The go-ahead rally began with singles by pinch-hitter Michael Cuddyer and right fielder Granderson against Avilan (2-2) before Lagares homered to left three pitches later.

"Amazing win," Lagares said. "The whole team battled the whole game. Doesn't matter the deficit, we never gave up."

Familia, who was away from the park Saturday following the birth of his son late Friday night, earned his 19th save after recording the final four outs to seal the Mets biggest comeback win in almost four years.

The Mets (34-30), who remained a half-game ahead of the Washington Nationals in the NL East, hadn't come back from a five-run deficit since Sept. 22, 2011, when they beat the St. Louis Cardinals 8-6 after trailing 6-1 in the seventh.

"You've got to play nine innings, you can't cash it in in the fifth or the third or the fourth," Collins said. "You've got to get out and compete. Even on the bench after we got behind early, got a couple runs back, got another run back, the energy on the bench was great."

The Braves (30-33) were decidedly less enthused after losing for the fourth time this season when scoring at least eight runs.

"We gave up some runs and couldn't stop them from scoring," Braves manager Fredi Gonzalez said.

The five-run blown lead wasn't even the biggest of the year for Atlanta, which had a pair of eight-run leads in a 13-12 loss to the Nationals on April 28.

The Mets and Braves combined for 28 hits on Sunday. Every position player starter had at least one hit except Braves shortstop Andrelton Simmons, who had four hits Saturday. Lagares and