Atlanta guard Jamal Crawford added 17 off the bench including the game's final six points, breaking a 96-96 tie at 2:14 to play with two free throws before adding a lay-up and late jumper to pull away from a subdued Celtics.
"An emotional game," Hawks center Al Horford told reporters. "We kept on fighting, kept on scrapping and this is big for us on the road, to be able to come back and beat a team like this."
Rajon Rondo recorded 26 points and seven assists and Paul Pierce put up 19 and eight rebounds for the Celtics (26-10), who lost to the Hawks for the third time this season -- they fell 93-85 to Atlanta (24-13) on Friday.
Boston shot 55 percent from the field including 10-for-20 in three-pointers but were plagued by 16 turnovers and failed to convert any big plays in the final moments.
The Celtics were again without defensive leader Kevin Garnett, missing his sixth straight game with a knee injury.
Offseason acquisition Rasheed Wallace, who had been starting in place of Garnett, also skipped the contest because of a sore left foot.
Without two key players, Boston's cause was also hampered by the ejection of coach Doc Rivers for arguing a call midway through the third quarter.
"It was just a terrible situation whether it was justified or not," said Boston veteran Ray Allen, who had 16 points. "After that, the game did change."
With the win, Atlanta pulled within one game of the Orlando Magic for the Southeast Division lead.
(Writing by Jahmal Corner in Los Angeles; Editing by John O'Brien)