"It worked out in the end," Delgado said.
Oliver Perez pitched six innings for his first victory in a month, and Aaron Heilman and Billy Wagner completed a six-hitter. Nick Evans had two hits and scored New York's first two runs.
Florida fell two games behind the NL East-leading Mets.
"We have a long way to go," said Scott Olsen (6-6), who gave up two runs in 5 2-3 innings. "We have a lot of games against each other."
Second-place Philadelphia won and remained a half-game back.
The Mets led 2-1 in the eighth when Delgado batted against Renyel Pinto in a lefty-lefty matchup with a runner on first and no outs.
Delgado has never had a sacrifice bunt, but he was 0-for-4 lifetime with four strikeouts against Pinto, and with three infielders shifted to the right side, he squared thinking he might push the ball up the third-base line.
"If he threw me something over the plate, I was going to try to get it down," Delgado said. "I'm not very good at it. That's why I kind of resist against it. ... I got scared when he came up and in."
Marlins manager Fredi Gonzalez said he wasn't surprised to see Delgado thinking about a bunt.
"Not really, because he hasn't had success against Pinto," Gonzalez said. "With no out, it didn't surprise me whatsoever. I wish he would have done it now."
The count reached 2-2 before Delgado pulled a pitch for his 23rd homer - his fifth against a left-hander.
"Delgado, left-on-left in that situation after he tried a bunt, that was big," Mets manager Jerry Manuel said with a chuckle. "That's OK, the bunt. I didn't mind the bunt, don't get me wrong."
The Mets liked the homer more.
"That was huge," Heilman said. "A three-run lead gives our pitcher room to be a lot more aggressive."
Heilman escaped a two-on, one-out jam in the seventh, then struck out the side in the eighth.
Wagner pitched a perfect ninth for his 27th save in 33 chances. He has allowed one hit and no runs in his past 10 innings.
Perez (7-6) left with a 2-1 lead and earned his first victory since June 29. He allowed five hits and walked three but shut out Florida over his final 5 1-3 innings.
"I'm thinking about trying to keep my team in the game," Perez said.
New York snapped a 1-all tie with a run in the sixth. Evans singled, took second on a walk to Delgado and scored on Carlos Beltran's two-out single.
David Wright walked ahead of Delgado's homer and scored in his 13th consecutive game, breaking Beltran's team record set in 2006.
The Mets opened the game with three consecutive doubles but managed to score only once. Jose Reyes tried to stretch his hit into a triple and was thrown out by left fielder Josh Willingham.
Evans doubled and scored on a double by Wright, but Olsen retired the next three batters.
Olsen didn't give up another hit until Evans' one-out single in the sixth.
Florida scored in the first on consecutive two-out doubles by Jorge Cantu and Willingham. But the Marlins, who rallied in the eighth inning Monday to beat the Mets, couldn't pull off another comeback.
"It's tough to do every night," right fielder Jeremy Hermida said. "You don't want to put yourself in that position every night."
Notes: The Mets improved to 21-11 against left-handed starters.... Reyes swiped second in the seventh for the Mets' 100th stolen base, most in the NL. ... The Marlins struck out 11 times, increasing their major league-leading total.
