Dan Uggla knocked in the other run for the Braves, who held on for a 6-5 victory in the opener to avoid their first four-game losing streak this season.
Julio Teheran (1-1) limited the Mets to one run on five hits and walked a pair over 5 1/3 innings to notch his first win in the majors.
Atlanta leads the NL wild card by 7 1/2 games over St. Louis. The Braves visit the Cardinals for a three-game set beginning Friday.
"This was a whole team out here today," said Ross. "Guys pitched well, played well, played good defense. It was nice to get out of here winning two games after that series in Philly."
Dillon Gee (12-6) gave up three runs -- two earned -- on four hits in six-plus innings to absorb the loss for New York.
"Maybe it's just the grind of my first big league season," said Gee. "Maybe I'm tired but everyone is tired and it's no excuse."
New York countered in the bottom of the first inning as Jason Bay plated Reyes with a sacrifice fly to center.
Atlanta regained the lead in the fifth when Martin Prado led off with a double and scored on Ross' one-out single up the middle.
Gee worked himself out of a bases-loaded jam in the sixth to keep it a 2-1 game.
The Braves got a sac fly from Jones in the seventh.
Ross put Atlanta up by three in the ninth with a one-out blast over the center-field wall. Bourn then slapped a two-out triple and scored on Jones' double to right.
Bourn tops the majors in stolen bases with 51...The Mets were 0-for-6 with runners in scoring position.