The no-doubt shot was estimated at 433 feet, making it the longest home run measured in the first 14 games at Miami's new retractable-roof home.
"That one was one of those no-doubters off the bat," said Stanton, who ripped into reliever Manny Acosta's first-pitch fastball. "First-pitch heater, right down the middle. I'm looking for a pitch that is going to get the heart of the plate."
Stanton's seventh homer of the season capped a three-hit day for the 22-year-old slugger, who used a pink bat as part of MLB's Mother's Day tradition of raising breast cancer awareness.
The last time the Marlins won via a walk-off slam came on June 11, 2008, when Dan Uggla connected.
The laser landed to the left of the park's ornate home run feature, which was set into motion with mechanical marlins spinning and water splashing. It was Stanton's third career grand slam, with his most recent one on July 6, 2011, against the Phillies.
Miami has shown a flare for the dramatic. Five times they've won by walk-off, including Greg Dobbs's game-winning single on Friday night.
After circling the bases, the 6-foot-5, 250-pound Stanton was lifted by teammate Logan Morrison.
"I didn't think he was going to get me," Stanton said. "I didn't know if his knees were going to hold up. We toppled, but it worked out."
Emilio Bonifacio completed the on-field party atmosphere by smearing a shaving-cream-covered towel on Stanton's face.
Nothing has been easy for the Marlins, who have now won four straight series.
"It's all about pitching," Marlins manager Ozzie Guillen said. "Late in the game, don't be surprised if we're going to win or lose late in the games. The reason is, our starting pitching is pretty good. You're going to see a lot of bullpen guys losing and winning games."
For the second time in the afternoon, the Marlins came back from being two runs down.
In the ninth, they rallied off closer Frank Francisco. Bonifacio led off with a triple, his second of the game. John Buck walked, and Brett Hayes entered as a pinch-runner. Dobbs, pinch-hitting, lined an RBI single, advancing Hayes to third.
Mets manager Terry Collins replaced Francisco, who felt the strike zone was squeezed. After handing the ball to Collins, Francisco walked directly towards home plate, shouting at umpire Todd Tichenor, who ejected the reliever.
Animated, Francisco gave Tichenor an earful before he headed toward the clubhouse.
"It's tough," Francisco said. "I went out there and Bonifacio hit a good fastball. I didn't care about Bonifacio. I was trying to shut it down right there, and I thought I was hitting my spots really good. I didn't get a call. Nothing you can do about that."
In his plate appearance, Buck felt there was one borderline call.
"The first [pitch], which started it, I thought it was pretty low, personally," Buck said. "Then, the next one was probably borderline. After that, they were in there. Trust me, I was hacking with Boni on third. We all know that I love to swing. I'm not the most patient guy. If I could have, I would have put some wood on it. There was probably one pitch, but other than that, I feel like no."
Jose Reyes had a game-tying sacrifice fly to center, and Acosta filled the bases by walking Hanley Ramirez and hitting Austin Kearns with a pitch. Stanton ended things one pitch later.
The Mets took a 4-2 lead in the ninth on Justin Turner's two-run double off Heath Bell.
Turner's heroics were reminiscent of the Marlins' 3-2 loss to the Mets at Citi Field on April 26. In that game, Bell surrendered two runs in the ninth inning on a day the Mets enjoyed a walk-off. The tying run scored when Turner capped a 13-pitch showdown with a walk.
In the ninth on Sunday, Daniel Murphy doubled with one out and Ronny Cedeno walked. A groundout advanced both runners into scoring position. Pinch-hitter Mike Baxter, who delivered pinch-hit hits on Friday and Saturday, was intentionally walked, loading the bases.
Turner, with the count full, lined a two-run double past diving first baseman Gaby Sanchez.
Miami right-hander Carlos Zambrano continued to put up terrific numbers without necessarily being rewarded.
Zambrano allowed two runs (one earned) in seven innings, striking out seven. The veteran lowered his ERA from 1.98 to 1.88. He came into Sunday having not allowed a run in his previous two starts, including a complete game.
Mets lefty Jonathan Niese held the Marlins scoreless over his six-inning stint.
Trailing by two in the seventh, the Marlins pulled even on Buck's two-run homer off reliever Ramon Ramirez. Bonifacio tripled to open the inning and Buck deposited the game-tying shot over the wall in left-center. It was his fourth of the season, and first at Marlins Park.
The Marlins used the long ball at opportune times to secure the series.
"We're still not even close to our full potential," Stanton said. "We're still getting it done somehow, every day. Once it clicks for everybody, we're going to be scary. Even in that road trip, we went 8-1 and we still didn't play our best baseball. More is yet to come."