"It was supposed to be a 2-1 pick-and-roll with Dwyane handling it and Mario [Chalmers] setting it, but they trapped and got us out of it well before we even got to that action," Heat coach Erik Spoelstra said.
"It was a broken play and we went from there."
Haslem hit the jumper in traffic from the left, then helped stop David West from scoring on the other side as time expired.
"That's what UD do. When he's in his spots on the court, he's going to shoot them. We expect him to do that. The shots he hit were big," said Wade, who had two 3s in the fourth that gave Miami a boost.
"I asked him after the game, 'How did you hit that?' It was one of those shots that we needed. The basketball gods were with us on that one."
The game-winner was the second basket for Haslem in the final minute and helped the Heat snap a season-worst three-game slide.
He tied the game at 100 with 45 seconds left, then after Marcus Thornton put the Hornets ahead with a free throw, Haslem won it with the off-balance shot.
"I just tried to make the shot, and focused in on knocking down the shot," said Haslem, who finished with 14 points. "We needed one. It was an up and down game and we had a couple of opportunities to put them away and to their credit, they kept fighting back."
Up by 11, the Heat couldnt halt a 10-0 run by New Orleans late in the third. West sparked it with 1:28 on the clock, and Thornton had a 3-pointer and a jumper to bring the Hornets within one."
The Heat missed 7 of their first 9 shots in the fourth quarter, seeing a three-point lead entering the period turn into a 95-91 deficit with 6:23 left when Stojakovic made a jumper. New Orleans hadn't led since the second quarter.
"We turned the energy up. We knew we had to fight back," Thornton said. "They were up eight points up and that's hard on the road but we pulled together and got it back within reach."
Thornton had 24 points and West added 13 for New Orleans, which is still without injured point guard Chris Paul.
New Orleans went more than 4 minutes without a field goal and Wade, who missed most of the first quarter with foul trouble, hit a pair of 3-pointers 1:33 apart, the second of which gave Miami a 98-95 edge with 3:44 remaining.
"Nothing came easy tonight because of the Heat and their defensive intensity and defensive emphasis. Nothing came easy for us other than a few small spurts," Hornets coach Jeff Bower said.
Like Wade, New Orleans had foul problems as well.
West, Emeka Okafor and Devin Brown watched from the bench for nearly 7 minutes with two fouls apiece in the first quarter for New Orleans, but Thornton provided a lift. He had 15 of the Hornets' 18 points in a 3-minute stretch in the first half.
Then Miami started rolling, a 14-5 run fueled by a 3-pointer from James Jones and two jumpers from Wade to go into the second half with a 59-52 lead.
Richardson remained sidelined with a lower back strain for Miami. Haslem returned after a two-game absence because of a aching left shoulder. ... Collison, who played for UCLA last season, said he doesn't mind having former USC coach Tim Floyd on board. "I knew what he was capable of. If there was one school that probably gave me more problems guarding me defensively, it would probably be USC. So I know his defensive schemes are on point," Collison said.