Tampa Bay started its rally when Desmond Jennings singled in Jose Lobaton with none out, followed by a fielder's choice groundout from Carlos Pena that brought in Elliot Johnson. That brought B.J. Upton to the plate, who wound up striking out.
"I think, especially for me in that situation, I definitely can't strike out," Upton said. "I got to make something happen."
Mets reliever Frank Francisco loaded the bases by walking Hideki Matsui, but a splitter that caught the bottom of the strike zone finished the game.
"You gotta hand it to him for having the guts to throw a 3-2 split right there, because he wasn't throwing them for strikes earlier in the inning," Zobrist said. "I wasn't looking for it, but I thought I saw it well enough to lay off it, and he put it in a good spot."
The start of the game was far from perfect for Tampa Bay, too. On starter Jeremy Hellickson's second pitch of the game, Mets rookie Kirk Nieuwenhuis blasted his fourth homer of the year over the right-field fence. It was the first leadoff home run of his career as well as the Mets' first in 2012.
In the top of the second, Jason Bay hit his own dinger -- his fourth on the year and first since April 20 -- to give the Mets a 2-0 lead.
Matt Joyce responded in bottom of the inning, when his double scored Matsui and Zobrist, tying the game. Three batters later, Elliot Johnson brought him in with a single to put the Rays ahead by one run.
That lead didn't last for long, as Lucas Duda hit a sacrifice fly with runners on second and third and one out in the third, scoring a tagging Jordany Valdespin. Ike Davis followed with a single that brought in David Wright to make it 4-3.
Zobrist came through in the bottom of the frame with a two-out double that scored Matsui to make things even yet again.
But Nieuwenhuis drilled a 1-2 pitch from Hellickson for a long ball that gave the Mets the lead for good in the fourth, this time to make it 6-4. After Valdespin was hit by a pitch and Wright walked, Duda picked up another pair of RBIs with his double. Maddon then elected to go to the bullpen, ending Hellickson's start after 3 2/3 innings. Hellickson allowed eight runs on nine hits, including three homers.
"They didn't miss too many mistakes," Hellickson said. "I left some changeups up, and they just didn't miss bad pitches."
He wasn't the only Rays pitcher to get roughed up in the Interleague series as the Mets scored 29 total runs, which left manager Terry Collins thrilled.
"I thought it was a tremendous job by our guys," Collins said. "You come in and face the best pitching in the American League and put up runs like we did, and good at-bats, and got their whole staff deep into the game with pitch counts. In the fifth and sixth inning, they were at 90 pitches. I was really pleased with the offense."
The Rays almost started their comeback in the bottom of the sixth after Mets starter Johan Santana loaded the bases with no outs. Collins brought in reliever Jon Rauch, who struck out Sean Rodriguez and pinch-hitter Lobaton before forcing Johnson to ground out to third.
"I was trying to make pitches in that tough spot and preserve the win for the team and just try to get outs," Rauch said. "If they want me to pitch in the sixth or eighth, whenever it is, just give me the ball and I'll try to do my job the best I can."
Santana went five-plus innings, allowing four runs on six hits and four walks with six strikeouts.