There was still plenty of time for Pierce and Rondo to come through.
Pierce scored 34 points in all, and Rondo had 16 points, 15 assists and nine rebounds in a career-high 52 minutes, 30 seconds.
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"We ask him to do a lot," Pierce said of Rondo. "We ask him to push it up, score and rebound. We ask him to do a lot because he can do it."
Pierce had four points in the first overtime -- putting him over 23,000 points in his career -- and eight in the second. Rondo, who played the entire first OT and all but 2 seconds of the second, had the only other basket in the second overtime before Courtney Lee made a pair of free throws with 6 seconds to play.
"I thought the biggest mistake I made was leaving Rondo in that long," Celtics coach Doc Rivers said. "I thought that had an impact on the speed of the game."
"I wasn't tired at all. You just can't turn the ball over. Look at the stats, man: nine turnovers out of 28," he said. "We had plenty of opportunities to take control of that game and win. We've got to be better in that area. We just can't turn the ball over."
Boston led by 14 in the third quarter and eight after the first basket in the fourth before Dallas chipped away at the deficit and tied it at 92 on Darren Collison's drive to the basket. After Rondo made a jumper, Fisher hit a 3-pointer with 1:47 left in the fourth to give the Mavericks their first lead of the game.
Pierce came out in the second overtime and hit a 3 to make it 108-105. Mayo's basket made it a one-point game and the tired teams struggled to score until Rondo drove to the basket to give Boston a 110-107 lead with 36 seconds to play.
From there, Dallas was forced to foul.
Pierce sank one of two free throws and Vince Carter hit a 3-pointer with 10 seconds left to make it 111-110. Pierce hit another pair of foul shots and Collison hit two free throws before Pierce and Courtney Lee each made two.
Mayo hit a meaningless 3-pointer at the buzzer to make it a two-point final margin.
The Celtics opened a six-point lead in the first quarter and lead by as many as 10 in the second before Dallas scored 8 of the last 11 points in the half to head into the break down just 48-43.
Boston opened a 14-point lead early in the third quarter before the Mavericks scored 10 of the next 12 points. After Rondo drove to the basket to give Boston a 78-70 lead with the first score of the fourth quarter, the Mavericks went on a 7-2 run -- five of those points coming from Mayo -- to make it a three-point game.
- Mavericks F Dirk Nowitzki has not played since October surgery on his right knee. Coach Rick Carlisle says there is no timetable for his return.
- The Celtics leave for a Texas swing, starting in Houston on Friday followed by San Antonio on Saturday.
- Mayo, who is second in the NBA in 3-pointers, did not make one until early in the second half.