After the Mets scored two runs in the eighth to tie it, Barraclough issued three straight one-out walks, and L.J. Mazzilli raced home with the tying run on Barraclough's wild pitch. Smith lifted a sacrifice fly to right, giving New York a two-run win.
Syndergaard brought plenty of heat early, with his fastball clocked between 97-99 mph. In 3 2/3 innings, the right-hander allowed two runs (one earned) on five hits with three strikeouts and a walk.
Syndergaard didn't have his best command, but he was able to minimize damage.
"I thought I was OK out there," Syndergaard said. "There were some things I was a little out-of-whack with here and there within the first three innings. Just some mechanical issues I was having that weren't allowing me to throw my breaking pitches for strikes. ... But I went out there and made some adjustments and was a lot happier."
Nicolino, meanwhile, was crafty, working four scoreless innings, striking out two while allowing three hits. The lefty kept the Mets off-stride with finesse. His fastball was 87-89 mph, but he was effectively working both sides of the plate and getting soft contact with his cutter.
Syndergaard and Nicolino were selected in the first and second rounds, respectively, in the 2010 Draft by Toronto.
The Marlins took the lead in the first inning on Justin Bour's two-out RBI single to right. Dee Gordon opened the inning with a single to center, and he stole a base. Gordon went 3-for-3 with two runs scored.
"I think it's good for Dee just to get going," Miami manager Don Mattingly said. "That's what we'd like to see as camp goes on -- him kind of getting into his rhythm, swinging the bat well and kind of doing his thing. We saw that a little bit today."
Gordon and the Marlins made Syndergaard throw 26 pitches in the first.
They took a two-run lead in the fourth, scoring an unearned run that was charged to Syndergaard.
Martin Prado singled with two outs off the Mets' right-hander, and lefty Jerry Blevins entered to face Ichiro Suzuki. But Blevins committed a throwing error trying to pick off Prado, who raced to third and then scored on Ichiro's single.
The Mets scored four times in the fifth inning off Jose Urena to claim a 4-2 lead. Travis d'Arnaud had a three-run double.
Miami regained the lead in the fifth, scoring three times. Gordon tripled, and Marcell Ozuna, Christian Yelich and Prado each collected doubles.
Up next for the Mets: The Tradition Field complex will be completely closed on Wednesday, with the Mets enjoying their lone off-day of the spring. It will reopen Thursday, before the Mets travel back to Roger Dean Stadium for another 1:05 p.m. ET game against the Marlins. Right-hander Jacob deGrom will start for New York.
Up next for the Marlins: Wei-Yin Chen, projected as Miami's No. 2 starter, will take the mound on Wednesday against the Nationals at 1:05 p.m. ET at Roger Dean Stadium. The lefty is expected to throw about 65 pitches. Jarred Cosart, who is in the mix for a rotation spot, will throw in relief. Right-hander Bronson Arroyo will be starting for the Nationals.