In his second inning of relief, Montero allowed a single to leadoff batter Kurt Suzuki, walked Ender Inciarte with one out and intentionally walked Freddie Freeman with two outs to load the bases. That brought up Kemp, who drove home a pair with a sharp double to left.
Braves closer Jim Johnson, who came on to pitch in a tie game in the 11th, also finished off the Mets in the bottom of the 12th to earn the win.
The game's first six innings belonged to former Mets teammates Jacob deGrom and Bartolo Colon, the latter making his first start since joining the Braves this winter.