The Braves were shoved to the brink of elimination in the National League East pennant race and also saw their lead in the wild card chase reduced to 3 1/2 games over St. Louis.
Wright hit a two-run homer as part of a four-run first inning and then added a three-run shot in the fourth.
Lucas Duda had four of the 20 hits and scored three times, helping the Mets end a six-game losing streak. New York's longest skid of the season has been seven games, which the Mets endured in the first month of the campaign.
Atlanta has seen its once firm grasp on the wild card berth loosened due to five losses in seven games.