Nowitzki scored eight of the Mavs' 12 points in overtime and finished the game with 33 plus nine rebounds.
Vince Carter scored 14 for Dallas, which won its third consecutive game and moved to within one game of the Los Angeles Lakers in the hunt for the final playoff berth in the Western Conference. O.J. Mayo scored 11 points, including a buzzer-beating jumper that sent the game into overtime.
The Clippers, who had won three of four games coming into Tuesday's game, were led by Chris Paul's 33 points. Blake Griffin and Caron Butler both added 14, but the Clippers hit only 10-of-33 shots from 3-point range and were 16-for-25 from the free throw line.
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