Paul Lo Duca, hobbled by a sore hamstring, hit a two-run single to break a scoreless tie in the seventh. Burnett (12-6) allowed six hits in eight-plus innings.
"All of the starters are feeding off each other," Burnett said. "You feel good about what's going on here. We're just riding it out."
Burnett set a Marlins record with his 49th career victory, surpassing former teammate Brad Penny, who will pitch for Los Angeles against Florida on Saturday. Burnett's career record is
49-44; Penny went 48-42 for the Marlins.
"As long as we go to the playoffs, that's all I care about," Burnett said. "I'm going to do what I can to get us there."
Florida trails NL wild-card leader Houston by a half-game.
The Marlins lead the major leagues with a club-record 15 shutouts, and their starters have an ERA of 0.85 over the past 10 games. Burnett's performance came after San Diego failed to score against Dontrelle Willis or Josh Beckett the previous two nights.
"I'd say they're letter-perfect," manager Jack McKeon said. "I could hang out at the barbecue stand if I knew they were going to do that every night."
The win gave McKeon the Marlins record for victories as a manager. He's 222-185. Rene Lachemann, the team's first manager, went 221-285 from 1993-96.
Burnett struck out nine, walked one and matched his career high for wins in a season. He took a four-hitter into the ninth but gave up consecutive singles and departed after throwing 112 pitches on an 87-degree evening.
"He's one of the best in all of baseball," Dodgers catcher Jason Phillips said. "He showed that tonight."
Jones came on to strike out all three batters he faced for his 27th save in 29 chances.
Florida won with only four hits. D.J. Houlton (4-7) retired the first 13 batters and took a shutout into the seventh, but the Marlins loaded the bases with one out and Lo Duca's single put them ahead.
"It was a lot of fun there for a while," Houlton said. "I had a good feeling out there, and I felt in command."
The rookie, winless since June 27, has lost six consecutive decisions. Los Angeles has scored a total of three runs in his past four starts.
"I can't do much about that," Houlton said. "I'm not going to hit anything, especially against A.J."
The Dodgers missed a chance to take the lead in the second. They loaded the bases with one out thanks to an error, a single, a double steal by Jayson Werth and Antonio Perez and a walk. Burnett escaped by striking out Phillips and Houlton.
Houlton was perfect for 4 1/3 innings before Juan Encarnacion lined a single to left. He was thrown out trying to steal.
Damion Easley led off the seventh with a double off the scoreboard for Florida's second hit. Carlos Delgado was intentionally walked with one out, and Houlton hit Encarnacion with a 3-2 pitch, loading the bases.
Lo Duca, playing despite a lingering hamstring injury, singled to right on the first pitch and limped to first base to put the Marlins ahead 2-0.
"He was hobbling around, but he's a gamer and he did the job," McKeon said.
Another run came home when the Dodgers failed to turn an inning-ending double play on Mike Lowell's grounder.
The Marlins improved to 28-27 against the Dodgers in Miami. ... The Marlins scored first for the 25th time in their past 30 games. ... Burnett has an ERA of 0.78 over his past six starts.