Minor (6-8) had an RBI single in the second for the game’s first run, then doubled and scored in the eighth.
Minor was perfect for four innings before Lucas Duda led off the fifth with a single that just barely touched the glove of leaping shortstop Andrelton Simmons.
The Mets didn’t have a runner in scoring position until Travis d’Arnaud opened the eighth with a double. Eric Campbell followed with an RBI single, finishing Minor.
Minor gave up four hits, struck out five and walked none.
Jonathon Niese (7-10) pitched into the eighth inning, when Atlanta scored twice for a 3-0 lead.
Pinch-hitter Ryan Doumit hit a two-run homer in a three-run ninth. Emilio Bonifacio got four hits, drove in two runs and stole a base.
Simmons drew a two-out walk in the second, Gerald Laird singled and Minor had a solidly stroked single to left for his fourth RBI of the season.
Niese had only allowed one run until Minor and the Citi Field wind helped Atlanta score twice in the eighth.
Minor led off the eighth with his fifth career double, a ball that the wind carried over the head of right fielder Curtis Granderson. Bonifacio hit a triple to center field that was also helped by the wind and scored on Freddie Freeman’s single.
The wind also boosted Doumit’s shot onto the bridge beyond the wall in right-center field. Doumit connected off Daisuke Matsuzaka, who came off the disabled list before the game.
Mets: The club remained without 2B Daniel Murphy (calf). He’s not healing as fast as the Mets had hoped, and manager Terry Collins didn’t rule out a trip to the disabled list.
Braves: Atlanta returns home from a 10-game road trip to begin six-game homestand tonight against Miami and Philadelphia. RHP Ervin Santana (13-7, 3.60 ERA) takes the mound against Marlins RHP Tom Koehler (9-9, 3.82). Santana is 2-0 with a 3.26 ERA in three starts this year vs. Miami.
Mets: Philadelphia will visit for a three-game series starting tonight. RHP Jacob deGrom (6-6, 3.13) pitches against Phillies RHP David Buchanan (6-7, 4.21) in a matchup of rookie pitchers.
On May 31, deGrom faced the Phillies at Citizens Bank Ballpark, giving up three runs and striking out 11 over 6 1/3 innings in a no-decision. The Mets handed Buchanan his first major league loss on May 29 and defeated the rookie a second time on Aug. 11.