Twelve pitchers appeared in the game, which saw the Mets let an early 3-0 lead get away.
Atlanta moved in front 4-3 in the seventh when Andrelton Simmons drove in a run with a fielder's choice grounder and the Braves were still in front heading into the ninth.
Wright, however, slugged a one-out homer off closer Craig Kimbrel, who suffered his second blown save of the season, and Atlanta then wasted a leadoff double in the bottom of the ninth.
Jordan Walden retired the first two Mets in the top of the 10th, but walked a batter and hit another before giving up the go-ahead single to Tejada. Murphy followed with his base hit off Luis Avilan.
Bobby Parnell (2-0) retired two batters in the Atlanta ninth to get the win and Jeurys Familia earned his first major league save with a perfect 10th.
The consecutive New York wins have come after a six-game losing streak.