Alex Gonzalez singled off Bobby Parnell (3-4) to lead off the ninth in a 5-5 game and went to second on a sacrifice. After Eric Hinske walked, Jones shot a 1-1 pitch through the right side of the infield for a run-scoring hit.
Gonzalez, Jose Constanza and Jason Heyward each homered for the Braves, who took the rubber match of a three-game series at Citi Field and have won three of their last four.
Jonny Venters earned the victory with a scoreless eighth and Craig Kimbrel notched his 34th save for National League Wild Card-leading Atlanta.
Braves second baseman Dan Uggla, meanwhile, extended his hitting streak to 28 games but rookie first baseman Freddie Freeman saw his 20-gamer snapped after going 0-for-4.
Jason Bay went 3-for-3 with three runs scored for the Mets.