"We struggled, pitching-wise, and Nate, obviously, didn't give us the start that we needed," Miami manager Mike Redmond said. "That's tough. You're down early in the game. We've been there before, playing catch-up from the fourth inning on."
The Marlins actually had chances to put up some runs against Bartolo Colon, who scattered 12 hits in 7 2/3 innings while giving up one run.
Miami did out-hit New York, 13-12, but the big blasts came off the bat of Flores.
"We had a lot of hits, but we didn't get any big hits," Redmond said. "They made their big hits count. They put some balls in the seats with guys in scoring position, and put up big numbers."
Miami is now officially eliminated from the National League East race, and is moving closer to being closed out of the NL Wild Card standings.
The Marlins maintain a one-game lead over the Mets for third place in the division with the series finale set for Wednesday.
The Marlins did strike first, cashing in on Reed Johson's leadoff double in the third inning when Christian Yelich drove him in with a two-out infield single.
But missed chances to add on in the third and fourth innings with runners in scoring position came back to hurt Miami.
The Mets responded with four runs in the fourth inning, all with two outs. Travis d'Arnaud doubled with one out, and Eovaldi put himself in position to get out of the jam unmarked after striking out Lucas Duda looking with the count full.
New York tied it on Flores' RBI double to left, starting a string of four straight batters reaching base. Curtis Granderson slapped an RBI single off second baseman Donovan Solano's glove into center. Matt den Dekker walked, prompting a mound visit by pitching coach Chuck Hernandez. Ruben Tejada broke the inning open with a two-run double.
"I just struggled finishing off the inning," Eovaldi said. "Flores hit that curveball. I've just got to do a little better job executing the pitches."
Eovaldi is at 186 2/3 innings, and the team would like to get him to 200. But now, they'll evaluate his next step.
"It's hard to say a guy is running out of steam when he is running up there 96, 97 [mph]," Redmond said. "He is up there with a career record for innings. He could be running out of gas, I don't know. The ball still seems to be coming out of his hands, but he's making mistakes, and they're making them pay. We'll have to figure out where we go from here."
Physically, Eovaldi says he is fine.
"I don't think it has anything to do with the season or the innings," he said. "It comes down to executing the pitches."
The Marlins squandered a bases-loaded, one-out chance in the fifth inning to chip back into the game. Colon worked out of trouble by striking out Marcell Ozuna looking before Garrett Jones tapped to short.
Eovaldi's struggles carried into the fifth inning, and the Mets once again were able to do major damage. This time it came with Flores' two-out, three-run homer off Brad Penny.
Daniel Murphy singled with one out, and Eovaldi was lifted after walking d'Arnaud. Penny struck out Duda, but Flores' connected on his three-run blast to left field, giving New York a six-run cushion.
Flores homered again off Penny in the seventh inning, blasting a two-run shot.
Prospect Andrew Heaney entered in relief in the seventh inning, his first big league action since he started at St. Louis on July 5. The lefty is a September callup.
"We haven't been hitting with men in scoring position, and having this kind of game, it feels good helping the team," Flores said. "Good pitches and good swings. They hung two breaking balls, and I was on it."