"Paul huddled everybody together before we came out of the locker room and was pretty vocal about what he wanted," Celtics coach Doc Rivers said. "He said if we came out strong defensively in the first four minutes, we could put them away."
Jefferson and Rajon Rondo broke the game open in the third quarter when they combined for 22 points and keyed a 14-0 run to go ahead 70-49 with 4:48 remaining.
"We knew their leading scorer was out," Rondo said. "Coach told us before the game that they were only four games out of the playoffs and we needed to be a spoiler."
Atlanta lost its first game without leading scorer Joe Johnson after winning four straight. The Hawks have also dropped seven straight on the road.
"We played nothing like we did the last four games," Hawks coach Mike Woodson said. "We played young and didn't play like a team pushing to make the playoffs."
Boston won for the fifth time in the past seven home games despite a 9-23 overall mark. It was the Celtics' most lopsided victory since Nov. 17 when they beat Portland by 28.
The Celtics eventually closed out the third with a Gerald Green 3-pointer for an 86-60 lead.
The Hawks had a brief comeback attempt thwarted when they started the fourth quarter with a 15-3 spurt after Sebastian Telfair hit a jump shot to keep the Celtics ahead 91-75 with 5:51 remaining.
"We knew they would make a big run," Jefferson said. "They had won four in a row and came back from a big lead last time we played them."
Atlanta erased an 18-point second-half deficit in their last visit to Boston in January.
Pierce had 17 points for Boston, which improved to 2-4 in its past six games against Atlanta.
Rondo gave the Celtics their biggest lead of the first half at 50-41 when he hit a half-court shot at the buzzer. He finished with 13 points and 10 assists.
Kendrick Perkins notched his third double-double of the season and second against Atlanta with 12 points and 12 rebounds.
"They wanted it more than we did tonight," Williams said. "We're still in the playoff race but can't take two steps forward and one backward."
Boston is 3-9 against the Southeast Division with its other two victories against the Charlotte Bobcats. ... Johnson missed his fifth game with a calf injury. ... Ryan Gomes missed his fourth game for Boston. ... Pierce recorded his 2,500th assist for the Celtics in the third quarter. ... After dropping 22 of 23, Boston is 6-3 in its past nine games.