Andre Miller had 21 points and five assists, and Louis Williams came off the bench to add 15 points on 4-for-6 shooting from the field for the Sixers, who have won 17 of their last 22 games.
Comfortably in seventh place in the East, Philadelphia (35-35) moved within a half-game of sixth-place Toronto and a game of fifth-place Washington.
New Jersey (29-41), meanwhile, dropped into a ninth-place tie with Indiana, 1 1/2 games behind eighth-place Atlanta.
"It was definitely a gut-check for us," Willie Green said. "It's great for our confidence being able to beat a team like New Jersey that's fighting for a playoff spot along with us."
The Sixers trailed by nine late in the third but held New Jersey to only 12 points in the final quarter. They shot only 38 percent overall, including 4-for-14 from 3-point range, but held the Nets to 38 percent shooting.
"It was a grind-it-out game," Sixers coach Maurice Cheeks said. "I thought after both teams playing last night, it was going to be a tough game for both teams. It was a gutsy win for us."
The Sixers, coming off an 18-point loss Friday night in Orlando, improved to 13-2 in the second game of their last 15 back-to-backs and 13-7 overall. They haven't lost consecutive games since the first week in February.
"It's focus," Dalembert said. "Last night's game was one of those games. Eighty-two games in a season -- there's going to be some games like that. We're mature enough to come back."
Said Cheeks: "It's something that we've been doing all season long. Trying to erase the memory of whether it was a win or a loss we've been very good at coming back in the game and getting ourselves back in the flow of playing again."
The Sixers led 49-42 at halftime after both teams, each coming off losses the night before, played poorly in the first 24 minutes. In a lethargic half, the Sixers committed 10 turnovers, while the Nets shot only 33 percent, including 2-for-11 from 3-point range.
Fortunately, Saturday night was "Sci-Fi night at the Sixers." Movie vignettes starring the Sixers players were shown on the overhead scoreboard during timeouts and often were more entertaining than the game itself.
"This was one of those games that was ugly for us," said Green, who managed just nine points on 3-for-17 shooting.
New Jersey woke up in the third and scored 13 straight to take a 66-58 lead. Carter muscled Miller into the paint and threw down a vintage dunk over Dalembert to give the Nets a 75-66 lead, their largest of the game.
"We had a real good third quarter," Nets coach Lawrence Frank said. "Our zone disrupted them a little bit, and Vince had a phenomenal attack. In the fourth quarter, they kind of flipped the script on us. Their pressure disrupted us."
The Sixers responded with an 8-0 spurt to regain the lead at 78-77. Marcus Williams followed with a 3 to put the Nets up one, but a three-second violation, offensive foul on Devin Harris and subsequent technical foul on Harris allowed the Sixers to go up 82-80 with 5:46 left.
"I wouldn't say we fell apart," Jefferson said, "but we might have had a couple of lapses."
Said Iguodala: "We got down by nine and came back and won the game, which shows a lot."
Miller spun by Marcus Williams for a layup, and Iguodala used a pretty crossover to get to the goal and give the Sixers an 86-83 edge with 3:34 to go. Dalembert preserved the lead with a nice block of Josh Boone in close, but Carter freed himself for a slam to make it 86-85 with 1:51 remaining.
The Nets missed key shots down the stretch, as Carter missed a jumper and a three-pointer, and Boone missed a layup. The Nets were just 5-for-21 in the final 12 minutes and hit just one of their five 3-point attempts.
"It came down to the last three minutes," Frank said. "Vince, make or miss we had some great opportunities right at the rim that didn't work out."
Iguodala hit four straight free throws in the final 25 seconds to help seal it for the Sixers. He was 10-for-12 from the line overall.
"I think we're starting to learn a little bit especially from other teams," Iguodala said. "I try to point out to the guys, let's learn from those great teams. Learn from the Detroits, learn from the Bostons. The things that they do well, we need to take that from them and incorporate that into our games. I think we're doing that, especially with the fourth-quarter defense."
The Sixers face the Celtics in Boston on Monday.
Philadelphia beat New Jersey for the first time this season. The Nets had won the first two meetings this season and last three overall. ... Lou Williams outscored New Jersey's bench, 15-12. ... Dalembert's right shoulder was wrapped after the game. He said he strained it in the second quarter.