Haywood tied it at 93 in the extra session and drew another foul.
Then it was deja vu.
Haywood missed the free throw again and Kidd-Gilchrist was there to keep it alive. That led to a Byron Mullens dunk, giving the Bobcats the lead with 2:21 left.
The Bobcats outrebounded the Mavericks 18-2 on the offensive glass in the second half and overtime, none bigger than the two by Kidd-Gilchrist.
"Those are the ones that are really just inexcusable," Mavs center Brandan Wright said. "You have to get a body on the guys. This one was a tough one to swallow."
Said Kidd-Gilchrist: "I'm just getting more comfortable I think as the season is going on. I think I'm starting to get everything. I really like my coaching. I'm just learning day by day."
Dallas coach Rick Carlisle stressed ball security coming in after the Mavericks turned it over 20 times in Friday night's 104-94 loss to the New York Knicks. But the Mavericks looked shaky early on, committing five turnovers in the first seven minutes to fall behind 22-9. They finished with 19 turnovers.
"We pretty much gave this one away," Wright said.
After a slow start, Mayo began to heat up, Carter hit three 3-pointers and the Mavericks opened a 55-44 lead at halftime. The Mavericks got a huge boost from their reserves, who outscored their counterparts 25-7.
Dallas' lead might have been even larger had it not been for Walker, who had 17 first-half points on 7-of-10 shooting.
Dunlap said breaking the losing streak against Dallas was huge for his team's confidence moving forward.
"There are a lot of first in terms of taking care of some things and we take full responsibility in terms of some of the things people see as a negative," Dunlap said. "We should be able to beat other teams that have had long winning streaks against us and we expect to beat them the hard way. We have to earn it."
NOTES: Haywood returned to the starting lineup after missing Friday's night game at New Orleans to deal with a family matter. ... Carlisle offered no update on when Dirk Nowitzki (knee) or Shawn Marion (knee) will return from their injuries. ... The Bobcats outrebounded the Mavs 36-20 in the second half and overtime.