Jordan Crawford put the Celtics up 91-90 with 1:36 to go but that proved to be the last field goal of the game.
Teague had a shot blocked by Avery Bradley on the ensuing possession but got the rebound and was fouled by Bradley. He dropped in both free throws for the 92-91 lead. Boston had five shots the rest of the way but missed them all, including a jumper by Crawford at the buzzer.
The Celtics led 83-72 with 6:28 to play before the Hawks started charging back with a 4-point play from Kyle Korver. Atlanta kept whittling away, finally catching Boston with 3:03 left when Mike Scott's layup made the score 86-85 Hawks.
No team led by more than one the rest of the way.
Paul Millsap had 34 points and 15 rebounds while Teague added 16 points and Korver 14 for Atlanta.
Boston got 21 points from Phil Pressey and 18 points and 10 rebounds from Kris Humphries.
Swim Week Miami Beach 2014 [PHOTOS]