Jason Kidd added 17 points for the Nets, who saw a 23-point third-quarter lead sliced to seven after going nearly five minutes without a point.
The Nets couldn't score in part because Bobcats assistant John-Blair Bickerstaff -- who took over as head coach when his father Bernie was ejected -- decided to repeatedly foul Collins, a 55 percent free-throw shooter.
The Hack-a-Shaq-like strategy nearly worked. Collins shot 3-of-10 from the line in the fourth quarter -- and one of the makes was banked in.
"I see it as an opportunity to get on the scoreboard," said Collins, who was in good spirits as teammates razzed him the locker room. "I look at it as free points. They tried to help my average.
"It's not like I don't practice. I take at least 200 free throws a day. It's a matter of making them in the game."
Carter bailed him out. His reverse layup and fadeaway jumper from the baseline put the Nets ahead 87-78 with 3 minutes left. New Jersey survived 12 missed free throws in all to win for the seventh time in nine games.
"Vince stepped up in a big way when we were struggling and had a great sense for the moment," Nets coach Lawrence Frank said.
New Jersey cruised early against the undermanned and poor-shooting Bobcats, who were without three key players and then lost Bernie Bickerstaff to a second-quarter ejection.
But Charlotte, with a mismatched lineup that included little-used Ryan Hollins, fought back under the guidance of John-Blair Bickerstaff, who at 27 is the youngest assistant coach in the NBA.
Hollins scored five of his career-high seven points in the fourth quarter.
"That's what I wanted to do, play hard," said Hollins, a second-round pick in last year's draft. "That's infectious. It rubs off on guys. I felt like I tried to give the team a lift. We made a run at it."
Raymond Felton had 18 points and five turnovers and Emeka Okafor added 14 points and 21 rebounds for the Bobcats, who shot 39 percent as they lost their second straight game after a three-game winning streak.
"The second half, the kids were terrific," said Bickerstaff, who was ejected for the first time this season. "They had the energy level. They could have easily surrendered."
Charlotte was without forward Sean May, who was plagued by pain in his right knee he had surgically repaired last season. He joined forward Gerald Wallace (right shoulder), who missed his seventh straight game and guard Brevin Knight (torn abdominal muscle), who sat out his 12th straight.
The Nets took control with a 16-3 run to close the first half. Kidd and Richard Jefferson hit back-to-back 3-pointers and Mikki Moore had an alley-oop dunk from Kidd during the spurt as New Jersey took a 53-34 halftime lead.
Bernie Bickerstaff may have had the best idea by getting tossed midway through the run. Upset with a foul called against Adam Morrison, Bickerstaff charged onto the court and picked up two technical fouls within seconds.
Carter had a spectacular one-handed dunk and a 3-pointer on consecutive possessions after back-to-back turnovers by Felton that gave New Jersey a 66-43 lead.
Kidd continued to show no ill-effects from going through a highly publicized divorce and rumblings that he might be on the trading block. He shot 6-of-13 and added seven rebounds and three assists as the Nets avenged a home loss to Charlotte in November.
The Nets started 11-17, but their recent hot streak has moved them within two games of .500 and to the top of the weak Atlantic Division.
"It's just find a way to win, by any means," Carter said. "We put ourselves in a hole, so we can't complain how the win looks. We just want to get back to .500 and into this playoff race."
Former Net Jeff McInnis had two points and three rebounds in 14 minutes, two weeks after he was traded to Charlotte. ... Moore, from nearby Gaffney, S.C., bought tickets for 26 friends and family members. ... The teams combined to miss 25 free throws. ... Longtime Charlotte Hornets public address announcer James K. Flynn was behind the mike and could permanently take over the job.