"We saw what we can do in one inning. We have to keep that confidence up tomorrow," Stanton said.
Mejia was charged with six runs and eight hits. New York starters had gone straight 11 games without allowing more than three runs.
Saltalamacchia's passed ball and Hechavarria's throwing error from shortstop let the Mets tie it in the bottom half.
Five hitters in New York's lineup entered batting .375 or better with at least one home run against Marlins starter Kevin Slowey. One of those was the 40-year-old Abreu, who made his second start for the Mets since getting called up Monday from Triple-A Las Vegas.
Abreu, who didn't play in the majors last season, hit a two-run shot in the first inning to give New York a 3-0 lead. It was his first big league homer since Sept. 28, 2012, with the Los Angeles Dodgers against Colorado.
"Feels good, man. A relief, I'd say, after one year off," Abreu said.
Shoddy defense by the Marlins led to New York's first run, on David Wright's sacrifice fly.
Derek Dietrich hit an RBI single in the second, snapping Mejia's scoreless streak at a career-best 14 2-3 innings.
NOTES: Slowey's previous outing at Citi Field was a memorable one. He struck out eight over seven shutout innings, setting club records for strikeouts and innings in a relief appearance, to earn the win in Miami's 20-inning victory last June 8. ... New York native Tom Koehler (2-1, 2.13 ERA) faces Mets RHP Dillon Gee (1-1, 3.58 ERA) in the series finale Sunday. ... Abreu is 8 for 20 (.400) with four home runs against Slowey. ... Mets manager Terry Collins won a replay challenge in the top of the ninth after Christian Yelich was called safe at first on a bunt. The ruling was overturned following a review that lasted 2 minutes, 8 seconds. ... Mets 2B Daniel Murphy was ejected by plate umpire Seth Buckminster for protesting a called third strike in the bottom of the 10th.