The Hawks came back from being down 17 points and held the Mavericks to just 12 points during the fourth quarter.
Atlanta outscored Dallas 21-8 in the final 10:23, according to ESPN Stats & Info.
Al Horford hit the game-winning shot with 4.2 seconds remaining.
Paul Millsap made a clutch three-pointer which brought the Hawks within one to put them in the position to win the game.
Jeff Teague finished with 25 points, 6 assists and 2 steals.