Mike Nickeas connected on a pinch-hit two-run homer for New York, while Hanley Ramirez collected a home run for Miami.
After falling behind by three runs, the Mets rallied back and took a 4-3 advantage with an unearned run in the sixth.
Jason Bay, who walked, scored with two outs when shortstop Donnie Murphy booted a grounder off the bat of Josh Thole.
In the eighth inning, a throwing error by reliever Steve Cishek led to the Mets tacking on another run.
Greg Dobbs, who had missed most of the Grapefruit League season with an injured left hamstring, singled in the ninth inning off New York reliever Manny Acosta to set up Tony Caldwell's game-tying single. After Dobbs moved to third on Donovan Solano's sacrifice bunt, he scored the winning run on Sammons' hit.
Ramirez put the Marlins on the board with a no-doubt home run off Miguel Batista to lead off the second inning. The drive to deep left-center field came on a 1-1 count. It was Ramirez's third home run of the spring, and it came on his final at-bat with the team stationed in Jupiter.
Batista tossed two innings, giving up one run on two hits, while logging 29 pitches.
Marlins manager Ozzie Guillen shuffled the lineup to get some extra at-bats for Giancarlo Stanton (left knee) and Logan Morrison (right knee). The two missed most of Spring Training due to injuries.
Stanton and Morrison batted first and second, respectively, to get more at-bats. For the rest of the lineup, Saturday was basically a short tuneup.
On the board in the Marlins' clubhouse before the game, it was written, "Show and go."
That was the message for a few of the starters, like Ramirez, Jose Reyes and Omar Infante. Each played two innings before getting the rest of the day to travel down to Miami.
More substitutions took place in the fourth inning.
The Marlins added two runs in the third inning, building a 3-0 lead on Morrison's RBI double and Murphy's sacrifice fly to center.
New York pulled even with three runs in the fifth inning. Lucas Duda doubled and scored on Thole's triple. Nickeas delivered the big blow off Mark Buehrle.
Up next: After pitching eight full innings in a Minor League game his last time out, R.A. Dickey will make his final spring tuneup Sunday in a 1:10 p.m. ET game against the Tigers at Digital Domain Park on MLB.TV. Dickey is scheduled to start the second game of the regular season on April 7.