The Braves won it against New York closer Jeurys Familia (1-1), who allowed his first runs of the season and failed in his effort to get a four-out save.
After pinch hitter Charlie Culberson struck out, Inciarte dropped a bunt down the first base line, and Camargo raced home with the game-winning run.
The winning pitcher was Jesse Biddle (1-0), who pitched a scoreless inning in his major league debut.
The Mets scored three times in the top of the eighth to break open a scoreless game.
Atlanta reliever Sam Freeman walked Wilmer Flores to open the eighth inning, and Jose Reyes was safe on a bunt single. Michael Conforto reached on a fielder's choice when Atlanta second baseman Ozzie Albies made an error while trying to turn a double play. The play was originally ruled an out but was overturned after a video review and loaded the bases for Yoenis Cespedes.
Shane Carle took over on the mound and got Cespedes to fly out, but Asdrubal Cabrera followed with a two-run single to right field to give the Mets a 2-0 lead. Jay Bruce drove the third run home with a single to center.
The Braves got two runs back in the bottom of the eighth on a Freddie Freeman double that almost left the park. Familia then entered with two outs and struck out Preston Tucker to end the threat.
For the first seven innings, the game was a pitching duel between New York's Jacob deGrom and Atlanta's Julio Teheran.
DeGrom allowed no runs on four hits and two walks. He struck out 10, giving him back-to-back double-digit strikeout games.
Teheran allowed no runs on four hits and one walk. He struck out six. It was the third time in five starts that he has not received a decision.
It was Teheran's second straight strong effort at SunTrust Park, where he had gone 4-10 with a 5.93 ERA in 20 previous starts. In his last two home starts, Teheran has allowed one run in 13 innings with 15 strikeouts.
--Field Level Media