Wisler (1-0), recalled from Triple-A Gwinnett before the game for what appeared to be a fill-in start, may have earned a longer stay in Atlanta. The right-hander allowed one run on two hits with no walks.
Kurt Suzuki had three hits and drove in three runs, including a two-run homer off Harvey in the first inning.
Todd Frazier opened the fifth with a homer over the 400-foot marker in center field for the Mets' only run off Wisler. Adrian Gonzalez led off the eighth with a homer off Lucas Sims.
The Mets, who scored nine runs in the eighth inning on Wednesday night to beat Washington 11-5, scored three in the eighth off Sims. His bases-loaded walk to pinch-hitter Brandon Nimmo forced in a run.
Harvey (0-2) allowed six runs in six innings. He retired 11 of the last 12 batters he faced and ended a streak of 12 consecutive starts, including his last nine starts of 2017, in which he failed to last longer than five innings.
Tucker doubled in two runs in the third and added a three-run double off Jerry Blevins in the seventh.
The Mets opened a 10-game trip with their first loss away from home this season. New York's 6-0 start in road games was the best in franchise history.
Freddie Freeman, who suffered no structural damage to his left wrist when he was hit by a pitch from Phillies left-hander Hoby Milner on Wednesday night, had two hits.
Wisler retired the first 11 batters before Asdrubal Cabrera singled in the fourth. Freeman made a diving catch of Jay Bruce's liner to end the inning.
Wisler was summoned from the minors because Atlanta's scheduled starter, Anibal Sanchez, was placed on the 10-day disabled list after straining his right hamstring while running in the outfield before Wednesday night's game against Philadelphia.
Johan Camargo, a defensive replacement at third base, made a diving catch in front of the Mets' dugout of Jose Reyes' short popup.
TRAINER'S ROOM
Mets: LHP Jason Vargas (broken right hand) is expected to make a minor league rehab start this weekend and could be recalled as soon as the following weekend. That has sparked speculation about how the Mets will make room for Vargas in the rotation. "It just so happens a starter is coming back and somebody is going to the pen," manager Mickey Callaway said.
Braves: Manager Brian Snitker said Sanchez already is showing improvement. Initial concerns were that Sanchez might miss several weeks, but now the Braves hope the right-hander's time on the DL may be shorter.
UP NEXT
Mets: RHP Noah Syndergaard (2-0, 2.95) will try for his first career win against the Braves when the series continues on Friday night. Syndergaard is 0-1 with a 3.92 ERA in four career starts against Atlanta.
Braves: LHP Sean Newcomb (1-1, 4.02) was 1-2 with a 2.70 ERA against the Mets as a rookie in 2017.
