"I think we're too young to even notice," Willis said after the Marlins built a big lead early and held off Atlanta's comeback in Friday night's 6-4 win over the Braves.
Florida's bullpen rebounded from a poor showing against the Mets with a strong effort to preserve the win.
Uggla hit his 25th homer, the most in major league history for rookie second basemen, as the Marlins won the first game of their 10-game road trip.
"It's big," said Florida manager Joe Girardi. "We need wins and that's the bottom line."
Willis (11-11) gave up nine hits and four runs in 7 1/3 innings. He gave up a leadoff home run to Marcus Giles, and went on to strike out six and walk two.
The Marlins pulled within 2½ games of San Diego, the NL wild-card leader.
"It's fun," said Willis of the wild-card race. "It's fun for baseball. This is how we want it."
But while Willis was confident the young Marlins would bounce back quickly, Uggla wasn't so sure.
"I'm not going to lie, the two losses to the Mets hurt," Uggla said. "They won the games in the last inning. You lose two like that, you feel like somebody shot your dog or something. We just had to come out twice as hard today."
The Marlins showed their resiliency early.
After Lance Cormier (3-5) walked Josh Willingham and retired Mike Jacobs, Cody Ross hit a sharp single to right that skipped under Francoeur's glove. Cabrera scored on the single, and Willingham and Ross scored on the error as Francoeur was slow retrieving the ball.
"I went down to get the ball and kind of picked my head up," Francoeur said. "It cost us the momentum of the game. It cost Lance some runs. It was a stupid mistake.
"I kind of set the tone. That's kind of tough to take when you know that you didn't help your team out that way."
Florida relievers went into the game with a 15-26 record, a 4.76 ERA and 25 blown saves. Taylor Tankersley pitched out of an eighth-inning jam and Joe Borowski pitched the ninth for his 34th save in 41 chances.
Tankersley, who blew a save chance Tuesday night against the New York Mets, gave up a sharp infield single to Francoeur. After a wild pitch moved the runners to second and third, Tankersley struck out Brian McCann and Martin Prado to end the inning.
"The tying run was on second with one out," Tankersley said. "The game was on the line. That's the job of an eighth-inning pitcher.
"It's awesome to be in a race like this. Every day in the big leagues is heaven to me."
Cormier gave up six hits and six runs in two innings. His poor start and the sloppy fielding by Francoeur left fans booing in the first inning.
The Braves began the day 6½ games behind the wild-card lead.
Hanley Ramirez doubled to lead off the game. He moved to third on Uggla's sacrifice bunt and scored on Miguel Cabrera's double.
Cabrera had three hits and raised his average to .342, moving two points ahead of Pittsburgh's Freddy Sanchez for the NL lead.
Giles hit his 11th homer in the Braves' first. Uggla hit a two-run homer in the second inning for a 6-1 lead.
Giles' broken-bat single drove in Prado and pinch-hitter Tony Pena in the Braves' second, cutting the lead to 6-3.
Willingham, who homered in three straight games against the Mets, was 0-for-3 with a walk.
- Uggla broke the homer record for rookie second basemen held by Joe Gordon, who hit 24 for the Yankees in 1938. Gordon finished with 25, but one of those came when he was not playing second.
- The Marlins' rookie home run record for any position is 26 by Preston Wilson in 1999. Another 2006 rookie, Willingham, also has 25 homers.
- Giles' homer was his fourth career leadoff homer, and his third of the season.