"Any time you lose a game you feel bad, but any time you lose a game that way because of your mistakes, it's worse," Hornets coach Monty Williams said. "(Dallas) hit some tough shots, but it was a lot of defensive breakdowns."
Anthony Davis added 10 points and 11 rebounds, but left the game in the third quarter with a sprained right knee.
Smith scored a season-high 22 points for New Orleans and Ryan Anderson had 20, including a 3 that gave the Hornets a 100-96 lead with 55.5 seconds left.
"Down the stretch tonight, you are up by four ... and you can't make plays," Williams said. "You can't blame anybody but yourself and that is basketball 101."
New Orleans led 69-63 on Smith's jumper about midway through the third quarter, but Dallas controlled the rest of the period while Gordon was on the bench and Davis was in the locker room with his knee injury.
Brand's 14-footer and Shawn Marion's alley-oop dunk ignited a 16-3 run, capped by Carter's 3, that put the Mavs up 79-72.
Davis eventually returned to the bench with more than eight minutes to go, and Hornets officials said he was available to return. But he did little more than pedal a stationary bike and watch the finish from the bench.
"I was prepared to play if they needed me. It's fine," Davis said, adding that he expected to play Sunday against Sacramento.
The Hornets managed to rally without him, thanks in large part to Smith, who scored six points during an 8-0 run that he started by converting a three-point play off an off-balance floater in the lane.
New Orleans led 97-94 after Smith's jumper, but Nowitzki stopped the surge with 15-footer that set up the thrilling finish.
NOTES: Marion and Mayo each scored 10 points. ... Dallas has scored 100-plus points in 16 of its last 18 games. ... The Mavs made eight of their 20 3-point attempts, while New Orleans went 5 of 17 from deep.