Harvey (6-1) took a no-hitter into the seventh inning before Jason Heyward broke it up with an infield single leading off the frame. The right-hander ended up notching his first victory since May 17, yielding three runs on three hits.
He exited in the eighth with a 4-0 lead after allowing the first three Braves batters to reach base, and the Mets bullpen barely hung on to secure the victory.
The New York closer tossed a scoreless bottom of the ninth for his 10th save as the Mets evened their five-game series at one win apiece.
Alex Wood (0-1) yielded one run on two hits over three frames in a spot start for National League East-leading Atlanta.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys