Delgado started for the Braves and gave up four hits, including a home run by Greg Dobbs, but was lifted after five innings. Cristhian Martinez, Eric O'Flaherty, Jonny Venters and Craig Kimbrel each pitched an inning of no-hit relief for Atlanta.
O'Flaherty, who pitched the seventh just before the Braves scored four times in the bottom of the inning, got the win and improved to 2-4. Kimbrel earned his major-league leading 44th save.
Dobbs connected on his eighth home run of the season in the second inning and Florida starter Ricky Nolasco (10-11) allowed just two hits through six innings.
Martin Prado followed with a nicely placed bunt single that got Uggla home. After another out, Gonzalez pulled a Nolasco pitch down the left-field line for his 13th home run of the year, making the score 4-1.