ATLANTA -- Even when his team was down to its last out, New York manager Terry Collins remained optimistic about a possible comeback.

"You get the sense that something big is going to happen," he said.

The New York Mets confirmed their manager's opinion when they rallied from three runs down with two outs in the ninth inning and scored three times with two outs in the 10th inning to beat the Atlanta Braves 10-7 on Sunday at Turner Field.

"Those two innings ... two outs and nobody on," Braves manager Fredi Gonzalez said. "They've got a good club. You open the door and they'll kick it in."

The Mets were down to their last out in the ninth when center fielder Juan Lagares doubled off Peter Moylan. Atlanta manager Fredi Gonzalez opted to bring in right-hander Ryan Kelly, who walked right fielder Curtis Granderson and gave up a long two-out homer to second baseman Daniel Murphy to tie the game.

New York worked more two-out magic in the 10th to secure the win. After Edwin Jackson retired the first two men he faced, he walked left fielder Kirk Nieuwenhuis and gave up a single to shortstop Ruben Tejada.

Catcher Kevin Plawecki hit a grounder to third baseman Hector Olivera, whose errant throw to second base pulled Daniel Castro off the bag and allowed Nieuwenhuis to score. Two other runs scored on bases-loaded walks.

"Just another great effort," Collins said. "We had the right guys up there. You have to tip your cap to them. They don't quit. It doesn't matter who's in there, they all want to be a part of it."

The Braves seemed to have the game put away when they scored three times in the eighth, one run coming on an RBI single by Castro and two more coming when Granderson lost Adonis Garcia's fly ball in the sun.

"A three-run lead and we couldn't put it away," Gonzalez said.

The winning pitcher was Bobby Parnell (2-3) and Addison Reed earned his fourth save with a scoreless 10th. Jackson (2-3) was the losing pitcher.

New York has won seven straight games and maintains a 9 1/2-game lead over Washington in the National League East. The win trimmed New York's magic number to 11 games and ensured the team of its first non-losing season in seven years.

It was the fourth straight defeat for Atlanta and the 12th straight home loss, the most since the 1914 Boston Braves.

It was the first time the Mets have swept a four-game series from the Braves since 1989, and the first time in Atlanta since 1985.

Braves starter Ryan Weber, making his second career start, pitched 6 1/3 innings and allowed four runs on five hits, with two strikeouts and two walks.

"I thought I threw the ball pretty well," Weber said. "I got a little tired toward the end and bad things happened to us."

New York starter Jonathon Niese got a no-decision. He pitched six innings and allowed three runs, two earned, on eight hits, with one walk and three strikeouts.

"Jon had much better command today," Collins said. "I'm hoping that's what we'll see out of him the rest of the way."

The Mets jumped out to a 2-0 lead in the second inning when third baseman Juan Uribe singled and left fielder Michael Conforto followed with a home run, his seventh, deep into the stands in right field.

The Braves came back to tie the game by scoring a pair of runs in the third. Garcia drove in right fielder Nick Markakis on a bloop single to right, one pitch after New York first baseman Lucas Duda failed to catch Garcia's foul pop near the first base dugout. Shortstop Andrelton Simmons drove in Castro.

The Braves took a 3-2 lead with a run in the sixth inning on center fielder Michael Bourn's sacrifice fly. The Mets regained the lead with two runs in the seventh as Granderson delivered a two-run single against reliever Matt Marksberry to put New York ahead 4-3.

Atlanta tied the game 4-4 with a run in the seventh against reliever Tim Stauffer. Castro and first baseman Freddie Freeman were on the corners after back-to-back singles. Castro scored when Garcia grounded into a double play.

NOTES: The Mets gave OF Yoenis Cespedes the day off on Sunday. In 39 games since joining the trade, Cespedes is batting .310 with 16 homers and 41 RBIs. Manager Terry Collins also said RHP Tyler Clippard and RHP Jeurys Familia were not available Sunday. ... Atlanta OF Cameron Maybin (corneal abrasion) missed his eighth straight game. Maybin is expected to return sometime during this week's three-game series against Toronto. ... The Braves continue their 10-game homestand with a three-game series with AL East-leading Toronto on Tuesday. RHP Julio Teheran (10-7, 4.38 ERA) will start the opener for Atlanta. ... New York returns home to open a nine-game homestand on Monday against Miami. Rookie RHP Logan Verrett (1-1, 3.06 ERA) will oppose Miami LHP Justin Nicolino (3-3, 3.72 ERA) in the opener.