"We were kind of bickering at each other a little bit too much, figuring out what defense we were going to run," Pierce said. "And I just had to say that the fight ain't with one another. It's against the other team on the court."
Pierce scored 17 of his 26 points in the third quarter as the Celtics erased a 19-point deficit and went on to consecutive wins for the first time since late November against Oklahoma City and Orlando. Rondo had 14 points, 11 rebounds and 10 assists.
Boston, which beat Indiana 94-75 on Friday night, had lost four straight road games.
Rivers insisted that despite the first-half struggles against the Hawks, the game plan would not change.
"I was like, 'This ain't it, don't get mad at Doc, he's coaching," Pierce said. "We've got to get mad at this other team."
Louis Williams scored 21 of his 28 points in the first half for Atlanta, which has lost two straight. Jeff Teague added 17 points, and Josh Smith, who was 2 for 12 in the second half, finished with 12 points and 10 rebounds.
The Hawks got off to a fast start, then fell apart in the third quarter as Boston began doubling ballhandlers on the perimeter and clamping down on Atlanta inside.
"They just climbed up in us defensively," Teague said. "They got physical and they brought pressure and got us out of our comfort zone. We just didn't respond."
The Celtics trailed by 19 with 6:20 left in the second, but went up 61-60 on Jared Sullinger's alley-oop layup with 3:47 left in the third. It was their first lead since the game's first minute.
Boston opened the third with a 14-1 run to pull within one. Hawks coach Larry Drew, whose team missed its first five shots from the field to begin the second half, called timeout at the 7:29 mark, but Teague lost the ball out of the bounds on the ensuing possession.
Atlanta, which had 13 turnovers and three assists in the second half, was just 2 for 14 from the field in the third and trailed 71-62 heading to the final period.
Kevin Garnett's fast-break layup with 8:53 remaining gave the Celtics their first double-digit lead at 79-68. Garnett finished with 14 points.
"The second half was completely different," Rivers said. "We worked the set. The first play went from one side to the other on offense. On defense they were late in the shot clock because Avery (Bradley) and Rondo both were up ball pressuring. And it changed the game for us."
Williams had outscored the Celtics 13-10 by the 5:47 mark of the first, connecting on his first seven shots from the field. His 16th point came on a layup for Atlanta's first double-digit lead at 23-12 late in the first.
But the Hawks could not overcome the absence of injured shooting guards Devin Harris and Anthony Morrow. Kyle Korver then fouled out with 6:37 remaining, and DeShawn Stevenson played only 13 minutes because of sore knees.
Drew called it "probably the most disappointing loss of the season" considering the Hawks have gone soft with big leads all season and backed down from the team that eliminated them in the first round of the playoffs last season.
"We've seen this kind of scenario before where we've played well and then when it starts to get more physical, we don't respond," Drew said. "That was clearly what happened tonight."
Jason Terry, in his first season with Boston and 13th overall, credited Pierce with backing up Rivers and straightening out the team's collective attitude.
"We took the challenge," Terry said. "We took it personal. You come in at halftime, and Lou Williams has 21 points, primarily all easy baskets. He was just letting them fly. So we wanted to invade his space. As we did that, we started to get more and more stops.
"Paul Pierce got it rolling. He really made his imprint on the game."
Korver fouled out for the first time in 27 games this season and finished with nine points. ... Atlanta scored 31 points in the first quarter, tying for the highest by a Boston opponent and the most since the Celtics opened the season Oct. 30 at Miami. ... The Hawks' nine points in the third were a season low by a Boston opponent. ... Harris missed his ninth straight game with a sore left foot. ... Morrow was sidelined for the fifth straight game because of a strained right hip.
Isaiah Thomas is starting for the Celtics on Thursday in Game 6 against the Hawks after experiencing no lingering issues after suffering a mild left ankle sprain in Tuesday's Game 5 loss.
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The NBA said Thursday that officials got it right when they didn't call a foul as Dwyane Wade tried to tie the score in the final seconds of Game 5, which the Heat lost to the Hornets 90-88.