Devin Harris added 26 points for the Nets, who have won two of their last three games. Jarvis Hayes gave 14 points and Josh Boone 12 in the win, one night after the Bobcats beat the Nets, 95-87, at the Meadowlands.
Gerald Wallace poured in 32 points, hauled in nine rebounds and dished out four helpers for the Bobcats, who had won four of their previous five games. Emeka Okafor chipped in 16 points and 10 boards, and Raymond Felton had 13 points.
Raja Bell, who left the game with a groin injury in the third quarter, ended with 18 points in defeat.
Boone's dunk and Keyon Dooling's three gave the Nets a 101-96 lead with 4:01 left in the extra stanza.
Three points from Okafor made it a two-point game, but Dooling hit a jumper and Hayes nailed a three to amp the Nets' lead up to 106-99 with 1:46 left.
The Bobcats failed to get within five points from there and the Nets pulled away.
The home team jumped out to a 26-22 lead after the first quarter, but the Nets managed to tie it, 47-47, heading into the intermission.
Two free throws from Carter gave the Nets a 61-58 lead with about 6 1/2 minutes left in the third quarter. Later in the third, three more free throws from Carter gave New Jersey a 70-62 cushion. Charlotte cut it to 72-66 heading into the fourth.
Trenton Hassell's three-pointer as the shot clock expired increased the visitors' lead to 77-69 with just under 10 minutes left in regulation, but Charlotte rallied.
Down by five with 5:41 left in the fourth, Wallace worked his way in down low and connected on a layup while getting fouled by Brook Lopez. He hit the free throw to make it 85-83.
After a botched Charlotte possession, the Nets took over with about a minute left. With 46.9 ticks showing, Harris was fouled and hit 1-of-2 to make it 94-93.
Okafor failed to sink a layup and Hayes grabbed the rebound and was fouled. He hit both from the stripe and it was 96-93.
Felton took the following inbounds pass, dribbled at the top of the arc and then drove in for a layup and got fouled before tying it at the line with 26.8 seconds showing.
The Nets failed to score on their final possession, and the game went to overtime.