Niese (9-6) controlled the Braves on six hits and struck outs six while issuing a pair of walks to collect the victory. The left-hander tossed 71 of his 106 pitches for strikes in the successful outing.
Ike Davis delivered a pair of run-scoring singles and Jordany Valdespin homered as the Mets built a 6-1 lead heading into the ninth.
Frank Francisco entered and issued consecutive run-scoring walks to pinch-hitter Juan Francisco and Michael Bourn before surrendering a two-run double to Martin Prado, pulling the Braves to within a run.
Jon Rauch then came in and struck out Jason Hayward, but the ball got away from catcher Rob Johnson and the throw to first barely nipped Hayward for the final out as the Mets avoided a three-game sweep.
Ben Sheets (4-2) was tagged for five runs (four earned) on eight hits over six innings for National League wild card-leading Atlanta.