Ronald Acuna Jr. homered off Rick Porcello to break a scoreless tie in the sixth and finished with four RBIs. Travis d'Arnaud added a two-run double for his latest clutch hit against his former team.
Wright went 6 1/3 innings and combined with three relievers on a three-hitter as the Braves took two of three in the series from the Mets, who entered Sunday leading the majors in batting average and on-base percentage.
The win was the second straight - and second in the majors - for Wright, who has allowed three runs and 12 baserunners over 12 1/3 innings in his last two starts after posting a 7.86 ERA and allowing 89 baserunners in his first 44 2/3 career innings.
''It's very encouraging to see him kind of get that confidence,'' Braves manager Brian Snitker said. ''That was impressive today. That's a really good-hitting ballclub that he was facing.''
Wright's recent surge has come at a key time for the Braves, who are looking for their third straight NL East title but have an uncertain back end of a potential playoff rotation. Atlanta is three games ahead of second-place Miami with seven to play after the Marlins split a doubleheader with Washington.
''I'm not too worried about it,'' Wright said about claiming a rotation spot in the postseason. ''Whatever the team wants me to do to help the team out, that's what I'll do.''
The loss damaged the postseason hopes of the Mets, who fell 2 1/2 games out of the final NL playoff spot with three teams to catch and only seven games remaining.
''Time is ticking away,'' center fielder Brandon Nimmo said. ''We don't have many more (games) to try and recover.''
Wright and Porcello were unlikely candidates for a pitchers' duel. They came in a combined 2-9 with a 6.45 ERA, but both entered the sixth working on a one-hit shutout.
Wright (2-4), who walked 20 batters over 25 innings in his first seven starts this season and had never pitched beyond the sixth in 10 career starts, retired the first eight batters before Wilson Ramos doubled down the left-field line. The 24-year-old right-hander set down the next 11 before walking J.D. Davis.
''I don't know that there's ever a bad time for a kid like that to find himself and get the confidence and get himself going,'' Snitker said.
Will Smith entered and got Dominic Smith to hit into an inning-ending double play.
The two-run double by d'Arnaud off Jeurys Familia provided insurance in the eighth. The catcher also singled in the sixth and finished the season hitting .479 (11 for 23) with three homers and 11 RBIs this season against the Mets, for whom he played from 2013-19.
''You wish he was on your team,'' Nimmo said. ''You wish you didn't have to play him.''
The Braves added four more in the ninth, when Acuna delivered a three-run double and scored on Marcell Ozuna's double.
Chris Martin walked one in the eighth and Mark Melancon allowed consecutive hits to Ramos and Nimmo before wriggling out of a jam in the ninth.
Porcello (1-6) took the hard-luck loss despite allowing just three hits and two walks while striking out 10 over seven innings. The 10 strikeouts were his most since he whiffed 10 while pitching for Boston against Philadelphia on Aug. 14, 2018.
The start was the 350th of Porcello's career. Only three pitchers who have debuted in the last 50 years - Felix Hernandez, CC Sabathia and Greg Maddux - have reached 350 starts at a younger age than Porcello (31 years, 268 days).
UP IN SMOKE
A fire broke out just beyond Citi Field during the Braves' four-run ninth inning. The smoke briefly enveloped the diamond in a charcoal-scented haze before sirens began echoing in the distance.
The singles by Ramos and Nimmo in the ninth cost the Braves a chance at another one-hitter against the Mets. Atlanta's last three one-hitters have come at the expense of New York, most recently on June 19, 2016, when Julio Teheran allowed a third-inning single to Michael Conforto in a complete game 6-0 win.
Mets: RHP Dellin Betances (lat) threw an inning in a simulated game Saturday. New York manager Luis Rojas said he was waiting to hear how Betances felt before considering what the next step might be. Betances last pitched on Aug. 29. ... The Mets sent INF Victor Gonzalez to Baltimore to complete a trade for reliever Miguel Castro, who was acquired Aug. 31. They also sent RHP Steven Villines to Texas to complete a deal for RHP Ariel Jurado, who was acquired Aug. 29.
Braves: RHP Huascar Ynoa (0-0, 5.30 ERA) is scheduled to make his second start since returning to the rotation and his fifth of the year overall when Atlanta heads home to begin a key series against the second-place Marlins.
Mets: RHP Jacob deGrom (4-1, 2.09 ERA), who is seeking a third straight NL Cy Young Award but lasted only two innings Wednesday due to a hamstring spasm, is expected to return as New York opens a series Monday against Tampa Bay.
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