NEW YORK -- The Miami Marlins staked Jarred Cosart to a big lead Monday night -- too big a lead, as it turned out.

Giancarlo Stanton's two-run homer capped the Marlins' seven-run second inning, but Cosart could not last through the fifth inning of what ended up being a 10-3 win for Miami over the New York Mets at Citi Field.

"Those are tough games to pitch in," Marlins manager Don Mattingly said, "You get the lead, now, all of a sudden, you're pitching to hold on to it instead of just staying aggressive in a nothing-nothing game. You know you've got to throw zeroes, you're not even thinking about that. But when you get a lead, for a younger guy, sometimes those are tough."

The Marlins led 8-0 entering the fourth, when the Mets scored all their runs.

"Obviously, to have that kind of a lead was comforting," Cosart said. "Kind of took the foot off the gas a little bit, which can hurt you, which it did for me a little bit today."

New York's first three batters reached in the fifth -- via an error, a fielder's choice and a walk -- before Yoenis Cespedes just missed hitting a three-run homer when the ball hooked foul.

Cespedes eventually hit a scorching liner to second for the second out, after which Mattingly exited the dugout and called on left-hander Chris Narveson to face left-handed hitting Mets first baseman Lucas Duda.

"Cespedes just hit a seed, just missed one foul," Mattingly said. "I can't give Duda a shot there (to) change the game."

Narveson fell behind Duda 3-0 before coming back to strike him out. The Mets only got one runner into scoring position the rest of the way against Narveson (who was credited with the win), Dustin McGowan, Craig Breslow and Bryan Morris.

Afterward, Cosart said he was more frustrated with forcing Mattingly to go deep into the bullpen than with not getting what appeared to be an easy win.

"Situation like that, you're trying to get through -- obviously, five would have been huge, but six, seven is ideal," Cosart said. "Only have to use two guys out of the bullpen instead of a couple more."

Cosart also took some satisfaction in watching his teammates force Mets manager Terry Collins to begin emptying his bullpen in the second inning, when Adeiny Hechavarria (two-run single), Dee Gordon (RBI single) and Christian Yelich (two-run single) gave the Marlins a 5-0 lead against Steven Matz before Stanton chased the left-hander with his two-out blast.

The Mets ended up using five relievers, including usual late-inning options such as Addison Reed, Jerry Blevins and closer Jeurys Familia.

"The positive is we got in the bullpen for them for this whole series," Cosart said. "That could be huge."

The loss was the first in seven big league starts for Matz while the seven earned runs were the most he's ever allowed as a professional. He gave up just nine runs in 35 2/3 innings for the Mets last season.

"I felt good out of the gates," Matz said. "The second inning got away from me really quick."

Hechavarria lofted a sacrifice fly in the third before Marcell Ozuna (solo homer) and J.T. Realmuto (RBI single) capped the scoring in the sixth. Realmuto had three hits while five other players -- Gordon, Yelich, Ozuna, Martin Prado and Chris Johnson -- all had two hits apiece for the Marlins (2-3).

Cespedes had two hits, an RBI and a run scored for the Mets (2-4), who have lost three straight. David Wright had two hits and a run scored. Cespedes and Wright have eight of New York's 15 hits in the last two games.

"Maybe it's where I sat, but we hit the ball pretty stinkin' good today," Collins said. "There were some loud noises and that was a very, very good sign. (Cespedes) hit the ball great. Wright hit the ball great."

NOTES: Mets RHP Jacob deGrom left the team Monday to be with his wife, who went into labor in Florida. Manager Terry Collins said he didn't know if the Mets, who are off Thursday, would place deGrom on the paternity leave list. ... Mets RHP Josh Edgin (Tommy John surgery) made his first rehab appearance Sunday, when he gave up one run in two-thirds of an inning for Class A St. Lucie. Edgin underwent the surgery on March 17, 2015. ... INF Chris Johnson drew his first start of the season at first base for the Marlins as left-handed hitting 1B Justin Bour sat against Mets LHP Steven Matz. ... The Marlins won their first replay challenge in the first inning, when LF Christian Yelich was originally ruled out on a chopper to third.