Uggla connected on a 3-2 pitch from Roy Halladay (5-3) while leading off the frame, sending it just over the left field fence into the stands to break a 2-2 tie.
Jonny Venters (3-0) picked up the victory with scoreless top of the eighth and Craig Kimbrel earned his 10th save in the ninth for the Braves, who took the rubber match of a three-game series with the National League East leaders.
Starter Tim Hudson yielded two runs on four hits over seven innings and Freddie Freeman drove in a pair of runs for the Braves.
Halladay absorbed his second straight eight-inning, complete-game loss. He held the Braves to three runs on eight hits, walking two and striking out seven.
John Mayberry smashed a two-run homer to account for the Phillies' runs.