Devin Harris added 26 points, and reserves Jarvis Hayes and Josh Boone added 14 and 12 points, respectively, for New Jersey, which improved to 10-4 in road games this season.
"It's kind of an 'us against the world' mentality," Carter said. "Coming into somebody else's building and wanting to get some roadkill ... it's good for us. Winning games like this, I don't care who the team is, will help."
The Nets are one of four NBA teams to have won 10 or more games on the road this season, and their road record is just behind defending league champion Boston and Orlando, both at 10-3. New Jersey is only 5-11 at home.
"With a team like ours, we need to put forth the extra effort," Harris said. "We need to win the hustle game and do the little things to push us forward a little bit more. ... We'll figure out the home thing later, but we just continue to get wins.
That's what we need to do."
Gerald Wallace scored 32 points. Raja Bell added 18, Emeka Okafor had 16 points and 10 rebounds, and Raymond Felton scored 13 points for Charlotte, which had defeated New Jersey 95-87 in East Rutherford, N.J., just 24 hours earlier.
"We played hard, we played aggressive and we did everything we could do to put ourselves in a position to win the game," said Wallace, who had 16 points in the fourth quarter alone as the Bobcats rallied from an eight-point deficit to tie it at 96 and force overtime.
However, the Nets opened the extra period with a dunk by Boone, followed by Keyon Dooling's 3-pointer, to take the lead.
"Boone had been struggling during the game ... but he comes out of a slip and gets a great dunk," New Jersey coach Lawrence Frank said. "You've got to give our guys a great deal of credit. They showed a great deal of grit and mental toughness."
Charlotte pulled within 101-99 on Okafor's dunk with 2:55 remaining, but Dooling hit a short jumper, followed by Hayes' 3-pointer, to kick off an 11-2 run that put New Jersey up 112-101 with 52 seconds left, its biggest lead of the game.
"Give them credit - they made plays," Bobcats coach Larry Brown said. "Vince found open people ... and we missed two layups to start overtime. Then we're playing uphill, and they made shots."
Charlotte, which had won four of its last five games, had a tougher time with the Nets in Saturday's game, swapping the lead six times and tying the score twice in the first quarter alone.
The Bobcats extended their lead to 10 points midway through the second quarter, with Nazr Mohammed's layup with 7:59 left putting them ahead 37-27. But New Jersey went on a 12-2 run, capped by Carter's 3-pointer, to tie it at 39 with 3:27 remaining.
Bell nailed a 3-pointer with 23 seconds remaining to make it 47-all at the break.
However, the Nets pulled ahead in the second half, going up 77-69 on Trenton Hassell's 3-pointer with 9:56 left in the fourth quarter. The Bobcats fought back to briefly lead, going up 87-85 on Wallace's three-point play with 5:12 left.
After tying the score twice, New Jersey pulled ahead 96-93 with 31 seconds remaining on a pair free throws by Hayes, but Felton's three-point play 5 seconds later sent the game into overtime.
Notes: Bell left the game with 3:20 remaining in the third quarter after he came up limping while battling for the ball under the Bobcats' basket. Team officials said he strained his left groin.
"We'll find out tomorrow exactly how bad it is," said Bell, who had averaged 7.6 points since joining Charlotte in a trade from Phoenix on Dec. 10. "It's pretty uncomfortable right now. ... When you're pitching in the way I was offensively tonight, you don't want to leave your teammates out to dry like that." ... The loss snapped Charlotte's streak of back-to-back series wins against the same team at six games, dating to the 2006-07 season. The Bobcats have one more back-to-back series against the same team this season, against Milwaukee on Jan. 2-3. ... Charlotte was whistled for two technical fouls Saturday - Brown with 2:19 left in the third quarter, and Wallace with 52 seconds remaining in overtime.
