Hanson (7-4) limited the Blue Jays to runs runs on five hits and one walk, while striking out four as the Braves clinched their three-game interleague series at Turner Field.
Uggla's three-run shot in the third inning broke a scoreless tie and put Atlanta ahead for good. Michael Bourn went 3-for-4 with an RBI for the Braves.
Toronto starter Drew Hutchison (5-3) was tagged for five runs on seven hits over 6 1/3 innings.
Jose Bautista socked a two-run homer, his 17th of year, for the Blue Jays.