Errors by reliever Jeurys Familia (1-3), center fielder Juan Lagares and third baseman Eric Campbell in the eighth helped the Braves rally from a 3-1 deficit.
Anthony Varvaro (3-1) pitched one scoreless inning to earn the victory. Craig Kimbrel recorded the final three outs for his 25th save.
The Braves announced late in the game that catcher Evan Gattis will be placed on the 15-day disabled list after an MRI revealed a bulging thoracic disk in his back.
Curtis Granderson had two hits, including a homer, for the Mets.
Trailing 3-1, the Braves loaded the bases with no outs in the eighth against Familia. Following singles by Justin Upton and Jason Heyward, Chris Johnson hit a soft grounder to Familia, who threw low to shortstop Ruben Tejada at second base for an error.
Tommy La Stella’s single up the middle drove in Upton, and Heyward scored the tying run when Lagares bobbled the ball in center for another error. With one out, pinch-hitter Ryan Doumit’s walk loaded the bases again. Campbell, the Mets’ fill-in third baseman while David Wright sits with a bruised left rotator cuff, bobbled Andrelton Simmons’ grounder for the third error of the inning, allowing Johnson to score the go-ahead run.
Dana Eveland replaced Familia and walked Freddie Freeman, pushing Atlanta’s lead to two runs.
Gattis, hitting .290 with 16 homers and 39 RBIs, missed his fourth straight game on Monday night with what had been called back spasms. The injury leaves rookie Christian Bethancourt, who made his first home start, and veteran Gerald Laird as the primary catchers.
New York’s Zack Wheeler was in position for the win before the Mets’ eighth-inning collapse. The Paulding County native gave up one run on four hits and five walks in 6 1/3 innings.
Wheeler walked at least one batter in each of the first four innings and also hit Bethancourt with a pitch in the second. The Braves were held without a hit until Heyward led off the fourth with a double into the left-field corner.
The Braves scored one run in the fifth. B.J. Upton, who hit a leadoff single and moved to third on Simmons’ single, scored on Freeman’s fly ball to left field.
Atlanta’s Alex Wood allowed three runs on six hits in six innings. He gave up runs in each of the first three innings and then recorded 11 straight outs.
Granderson opened the game with his 11th homer. It was his 26th career leadoff homer.
Travis d’Arnaud’s double drove in Chris Young, who reached on a single, in the second. Young’s fly ball in drove in Daniel Murphy from third base in the third.
Mets manager Terry Collins successfully challenged a ruling that B.J. Upton stole second base in the third inning. The safe call was overturned following the review, which lasted 1 minute, 15 seconds. Upton’s slide easily beat the throw, but the replay showed he was tagged when he bounced off the bag at the end of his pop-up slide.
Running from right field, Heyward made a sliding catch in foul territory on Tejada’s fly ball to open the fifth.
NOTES: Fans with tickets to tonight’s game can arrive early, with gates opening at 3:30 p.m., to see the U.S.-Belgium World Cup game on the video board. ... Collins said Wright will avoid the DL, but will remain in New York for rest and treatment during the Braves series. Collins hopes Wright is ready to play Friday when the Mets open a home series against Texas. ... RHP David Carpenter (strained right biceps) struck out each of the three batters he faced for Triple-A Gwinnett on Monday in what is expected to be his last rehab appearance. Carpenter can come off the 15-day DL on Wednesday. ... Braves LHP Mike Minor will face Mets RHP Daisuke Matsuzaka in tonight’s second game of the series.