Nowitzki made a pair of free throws to open overtime, giving Dallas its first lead since it was 6-4. He followed with a jumper, and after a free throw by Brandon Bass, Nowitzki buried a 3-pointer, pumping his fists in the air after giving the Mavericks a 120-112 lead.
Howard followed with his two baskets, part of Dallas' closing 19-2 run. The Knicks didn't have a field goal after Richardson's basket with 2:28 remaining in regulation that made it 112-105.
Jason Terry scored 16 of his 20 points after halftime for the Mavs, who avoided their first six-game skid since Feb. 29-March 9, 2000. Reserves James Singleton and Brandon Bass each added 12.
Zach Randolph had 27 points and 18 rebounds for the Knicks, who were 0-for-9 in overtime and lost for the first time this season when scoring 100 points.
Quentin Richardson had 17 points and Chris Duhon added 16 points and 12 assists. Jamal Crawford also had 16 points.
The Mavericks went with a small lineup in the second half, matching up with the Knicks by benching starting center Erick Dampier. Terry scored 14 points in the period in the third quarter, trimming it to 91-89 heading to the fourth.
The Mavs were down two again midway through the fourth after scoring seven straight, but David Lee had a basket before Richardson nailed a 3-pointer to push it to 110-103 with 3½ minutes to go. Dallas responded again to make it 112-110 on Nowitzki's bucket with 1:27 remaining, and finally pulled even on Terry's jumper with 38 seconds left.
After a couple of misses by Richardson, the Mavs called a timeout and got the ball to Terry, who was short on a jumper from the top of the key.
The Knicks made seven of their first eight shots and had an answer for every Dallas rally for most of the game. But the Mavs scored the final seven points of regulation, fighting for loose balls and crashing the boards in desperation.
Randolph made first seven shots and New York shot 60 percent in the first quarter, leading by as much as 13 before settling for a 35-26 advantage. The Knicks, pushing the pace at every opportunity, opened a 15-point cushion just under halfway through the second on David Lee's basket.
But with Wilson Chandler on the bench with a third foul, the Knicks had no answer for Nowitzki, who broke free for 13 points in the final 6:05 of the half as Dallas cut it to 64-57 at the break.