"Any time you can spend a birthday in the Major Leagues, that's enjoyable," said LeBlanc, who opened the season at Triple-A. "It's just icing on the cake that I got to pitch and we got the win."
Chad Gaudin, Carlos Zambrano, Mike Dunn, Heath Bell and Steve Cishek silenced New York over the final five innings.
Zambrano, who worked 1 1/3 innings, was credited with the win, while Cishek collected the save.
"I'm keeping the team in the game," LeBlanc said. "I'm giving the team a chance to win. I'm not going as deep as I feel like I should, with the pitch counts they're giving me. That falls on me and being efficient and pounding the strike zone and being aggressive."
Jose Reyes slapped an infield single in the fourth inning, increasing the longest hit streak in the Majors this year to 25 games. It's already a personal best for Reyes, which tied Kevin Millar for the third-longest stretch in Marlins history. Millar reached 25 games in 2002, the same year Luis Castillo established the club record with 35. Emilio Bonifacio had a 26-game streak a year ago.
Still, there is a little concern with Reyes, who jammed his right hand last Friday in Washington. He had the hand iced after the game, and manager Ozzie Guillen is weighing whether to play Reyes on Wednesday.
"Right now, his hand is really sore," Guillen said. "I'm kind of worried about him for tomorrow. He should be fine. We'll see what he can do."
Reyes says it bothers him more to bat right-handed than from the left side, and he was up against lefty Jon Niese on his 1-for-4 night.
"From the right side, if I get jammed, it's going to hurt," Reyes said. "From the left side, it's all right. It's no big deal."
Giancarlo Stanton, reinstated from the disabled list, was in the lineup for the first time since July 7. He added a sacrifice fly in Miami's four-run fourth inning against Niese.
For the second straight start, LeBlanc was on a pitch count. When he reached 85 after Daniel Murphy homered to open the fifth inning, the lefty was lifted, three outs shy of qualifying for a win.
"I know he was disappointed," Guillen said. "He had a chance to win this game, but in the meanwhile, I have a job. Make sure we stay with the pitch count. Next time, he should be able to go seven innings."
In his previous start, on Aug. 1 in Atlanta, the left-hander was taken out after 4 1/3 innings, when he was at 71 pitches in a game Miami was leading.
The Marlins are gradually building up LeBlanc's pitch count because he had been used exclusively in relief after being called up from Triple-A on July 1.
"It's not [Guillen's] fault, it's my fault I couldn't get three outs in a less number of pitches," LeBlanc said.
In four-plus innings, LeBlanc allowed one run on six hits with four strikeouts.
The Marlins claimed the lead with four runs in the fourth inning. Justin Ruggiano and Reyes each singled, and Carlos Lee ripped an RBI single to left, extending his hitting streak to 12 games.
"It's frustrating. I made some pretty bad pitches," Niese said. "I hung my curveball on three consecutive guys, which really hurt me. That's been my Achilles heel this year is giving up those big innings. That's something I've just got to work on."
Stanton lined a sacrifice fly to deep center, and Buck delivered a two-run double.
"Definitely, it feels good to get the bat going a little bit and help the team," said Buck, who had a two-hit night. "To do it timely, that was a good day, I guess."
New York countered with two runs in the fifth inning. Murphy led off with the homer to right, and Gaudin came in for LeBlanc. With two outs, Gaudin issued three straight singles. Andres Torres collected an RBI on his single to right.
"LeBlanc threw really well," Buck said. "Tonight was probably some of his better stuff that he's had. His control, normally, he's hitting the gnat out of my glove. That was maybe off a little bit. But his stuff was moving really well."