"We had a horrible, horrible third quarter," Miami coach Pat Riley said.
Wade was sidelined after straining his right wrist in a loss Wednesday, and O'Neal has sat out the past 23 games with a knee injury. Also missing was reserve forward James Posey, who served a one-game suspension for a flagrant foul.
"We're hurting right now," Heat forward Antoine Walker said. "It's unfortunate. We've got to try to keep our head above water."
New Jersey snapped a four-game losing streak.
"Winning is always good," guard Jason Kidd said. "It's the best deodorant."
Miami built a 49-46 lead, but during the next 5½ minutes the Heat went 0-for-4 with eight turnovers, while New Jersey went 10-for-11 to take a 67-49 lead.
"Definitely it was defensive oriented," said the Nets Vince Carter, who finished with 23 points, nine rebounds and six assists. "We created our offense through easy baskets. That's the style of basketball we can put on the floor."
The poor stretch by the Heat followed a spirited first half when they led by as much as six points.
"In the time between the walk to the locker room and the walk back to the court, I don't know how it happened," center Alonzo Mourning said. "You'd have to ask some of my teammates."
The Nets' Richard Jefferson scored 22 points, including eight during their 21-point run. New Jersey scored on five consecutive possessions, missed a shot, then scored on the next five possessions, with Kidd's 3-pointer capping the surge.
During the same stretch, Miami committed a turnover on four possessions in a row.
"We had a lot of mistakes on both ends," Heat forward Dorell Wright said.
Kidd had 17 points, 10 rebounds and seven assists for the Nets, who had lost both previous games against Miami this season. Three-pointers by Kidd and Bostjan Nachbar helped New Jersey maintain a comfortable cushion in the final period.
"It's all about confidence," Carter said. "Guys have been struggling. We played good basketball tonight, and hopefully that carries over."
Wright sparked the Heat's strong start. He finished with 21 points, six blocks and four steals, all career highs.
"If there's a silver lining in this whole thing, it's his development," Riley said. "He's a bright spot right now for us."
Miami finished with 18 turnovers, including six by Walker. Jason Kapono, who replaced Wade in the starting lineup, totaled only eight points.
The Heat fell to 0-3 this season without Wade, who may also sit out Saturday's game at Orlando.
"Missing is missing two of the top five players in the league," Nets coach Lawrence Frank said. "But you never know how a game is going to be determined. We needed to find a way to win a game, and we did."
- The Heat fell to 8-8 at home. Last season they went 31-10 en route to the NBA title.
- The Nets improved to 2-14 when fail to score at least 100 points.
- The Heat are 5-0 on Saturdays going into the game at Orlando.