Uggla -- who also homered in the seventh -- followed with a decisive run-scoring single to left.
The Braves added another tally on B.J. Upton's sacrifice squeeze, wrapping up a victory in a game suspended by rain Friday in the eighth inning at 5-5.
The Mets had rallied for two runs in the eighth, capped by Ruben Tejada's score on a wild pitch from Anthony Varvaro (2-0) during during a rainstorm.
Evan Gattis' two-run single earlier in the eighth had put the Braves up 5-3.