The teams combined for just six points in the extra period and there was no scoring for the final 2:25 after Kirk Hinrich hit a jumper for the Hawks.
Josh Smith misfired from 3-point range on Atlanta's final chance to win it with 4 seconds left.
Rajon Rondo paced the Celtics with a triple double that consisted of 10 points, 10 rebounds and 20 assists.
Boston won its fourth in a row and maintained a three-game lead over Philadelphia in the Atlantic Division.
Kevin Garnett had 22 points and 12 rebounds for Boston, but fouled out with 2:43 to go in overtime. Bass scored 21 points and had 10 boards.
Atlanta was paced by Jeff Teague with 21 points while Josh Smith had 20 points and 11 rebounds. Atlanta had won three straight.