Ray Allen had 21 points for the Celtics, beaten by the Mavericks 99-90 in Boston on Jan. 18 in their only other meeting this season.
Boston's Rasheed Wallace vowed "retribution" in the rematch, complaining after the game in January that the referees give Dallas' top scorer Dirk Nowitzki preferential treatment. Wallace refused to comment after Saturday night's game, but Rondo said the Celtics weren't dwelling on the past.
"We don't look at it as payback," Rondo said. "That game was over when it happened. It's a new time for us and we just needed a win."
Nowitzki had 37 points in the first meeting, but Boston's Kevin Garnett, a longtime Nowitzki nemesis, missed the game with a hyperextended right knee. Had he been healthy, Garnett would have been the primary defender on Nowitzki.
This time, Garnett and Wallace took turns guarding Nowitzki, who still went 11 for 19 from the floor and finished with 28 points.
Nowitzki had 12 points in the final quarter, but teammates were only able to provide nine more.
Garnett finished with eight points, nine rebounds and a season-high five steals.
The Celtics were coming off Friday night's 94-87 victory at Houston. The Mavericks had been off since Wednesday night's 113-106 home win over Chicago.
"They had three days off, had prep time for us, and we played last night, so to come back at the end and take the game away from them was huge for us," Boston coach Doc Rivers said.
"It's frustrating," Terry said. "These are games we've been winning."
The Mavericks led by seven early in the fourth quarter, but Rondo converted layups on three straight Boston possessions down the stretch, giving the Celtics a 94-91 lead with 2:47 left.
Pierce drained a 3-pointer from the top of the key and Rondo scored on a layup to put Boston in front 99-93 with 1:18 remaining.
"Rondo was the key down the stretch," Dallas center Brendan Haywood said. "He made plays and they really fed off his energy. We didn't get the stops. We didn't do enough."
Boston went 12 for 17 from the field in the fourth quarter, with Rondo hitting all five field-goal attempts and scoring 10 points in the quarter.
"He kept getting in the lane and he hit some outside shots," Mavericks coach Rick Carlisle said. "He's crafty and knows how to take advantage of you [defensively] favoring other guys."
Allen hit a pair of 3-pointers to help Boston open the third quarter with a 13-5 run for a 61-52 advantage.
Pierce scored eight of Boston's last 10 points in the third and the Celtics took a 73-72 edge into the fourth quarter.
Dallas G Jose Juan Barea missed Friday's practice with an illness, but he was in uniform 24 hours later, scoring three points in 12 minutes. ... Boston has won five of the last six against Dallas. ... Both teams committed 18 turnovers.