Smith's basket with 41.9 seconds left gave Atlanta the lead for good after the two teams had battled for the advantage throughout a game that featured 19 lead changes.
Smith finished with 19 points and 13 rebounds, and Joe Johnson scored a game-high 28 points for the Hawks.
The Bucks dropped their fourth game in six contests despite 21 points and 11 assists from Brandon Jennings.
Mike Dunleavy contributed 17 points for Milwaukee.
Notable deaths of 2014 [PHOTOS]