Monta Ellis scored 19 points and made a pair of jumpers early in overtime before consecutive 3-pointers by Chandler Parsons and Nowitzki made it 96-88 with 34 seconds to play. That gave Nowitzki 15 points for the game and 27,412 in his career, moving him past Moses Malone into the No. 7 spot.
Rajon Rondo shot 1 of 13 for two points but added 14 assists and 10 rebounds for the Mavericks, who have the longest current winning streak in the NBA. Tyson Chandler finished with 14 points and 13 boards.
Brook Lopez had 22 points and 13 rebounds for the Nets but faded after an 18-point first quarter. Jarrett Jack had 20 points and 10 assists.
The Nets were without Deron Williams (sore left side) and Kevin Garnett, who rested on the second night of back-to-back games, and dropped their second straight after winning three in a row.
Dallas hadn't trailed by more than seven points in any of the first five victories, but was down 14 after one in this game. But the Nets managed just 30 points in the second and third quarters after scoring 35 in the first 12 minutes.
The Mavs ran off the first 10 points of the fourth, taking a 75-65 lead on a 3-pointer by former Nets forward Richard Jefferson. They led by 11 with under 7 minutes remaining in regulation, but then didn't make a field goal after Ellis' basket made it 80-71 with 5:28 left.
Brooklyn battled back to grab an 82-80 lead on Jack's jumper with 26 seconds to play before Ellis tied it with two free throws with 10.5 seconds remaining. Joe Johnson missed a jumper that would have won it in regulation.
Ellis made the first two baskets of OT, Chandler had a follow shot and a pair of free throws, and Parsons and Nowitzki put it away from beyond the arc.
Nowitzki is 10th on the combined NBA-ABA list, where Malone remains seventh. The German forward became the top foreign-born scorer earlier this season.
Mavericks: Dallas is 11-0 on the road against Eastern Conference teams and has won 15 in a row dating to last season. ... Dallas also won six straight from Nov. 11-21. ... Jefferson is third on the Nets in their NBA history in points and minutes played.
Nets: The Nets haven't beaten Dallas four straight times since February 1998 to March 2000. ... The Nets held a moment of silence before the game for former New York Gov. Mario Cuomo and Stuart Scott, the longtime ESPN personality and "SportsCenter" anchor, who both died in recent days.
Mavericks: Host Detroit on Wednesday.
Nets: Host Boston on Wednesday.