The Braves won their third straight, with Tommy Hanson and Kris Medlen combining for a six-hitter.
Atlanta was clinging to a 2-1 lead heading into the seventh, but Uggla doubled home two runs and then scored along with David Ross on a single by Jones.
Hanson (3-2) gave up a run on six hits with three walks over six innings to get the win. Medlen allowed only one base runner during the final three innings to collect the first save of his career.
A.J. Burnett (1-1) suffered the loss despite giving up only two runs in six innings. Atlanta's big seventh inning was put together against relievers Tony Watson and Evan Meek.
The Pirates have lost four times in their last seven games.