Jaylen Brown scored 32 points and Jayson Tatum added 30 as the Celtics won the best-of-seven series 4-2.
The Celtics are the top seeds left in their conference after the Miami Heat’s shock win over the Milwaukee Bucks.
In a contest featuring 22 lead changes, Trae Young, whose late three-pointer sealed victory for the Hawks in the previous game, scored 30 points with 10 assists.
However, just five of those points came in the second half as Atlanta faded as the game wore on.
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A run of 11 unanswered points in the fourth quarter, including three straight three-pointers from Brown Tatum and Al Horford, saw the Celtics take a grip on the game that proved decisive.
“We talked about finishing the game,” Horford said.
“I felt the last game, for the most part, we were fine but tonight there was that sense of urgency. We understood how important it was to not extend the series.”
Game one of the Celtic’s semi-final against the 76ers takes place in Boston on Monday.