Kidd had 22 points, 13 rebounds and 10 assists despite playing with a cracked rib that the Nets revealed on Thursday. It was Kidd's ninth triple-double of the season, tying his personal high, and his sixth against the Kings.
Carter led the Nets with 26 points. He also had 11 rebounds.
The two All-Stars were rumored to have been on the trading block before Thursday's trade deadline.
"The guys weren't really worried about that," Carter said of the trade talk. "You guys made a big deal of it. We were just trying to get ourselves back on track."
Kidd, who has also been hampered by a sore back, produced a vintage performance to help the Nets end the losing streak.
"That's why this guy is so different," Nets coach Lawrence Frank said. "It takes a whole lot for him not to play. That is a rarity in all sports. He doesn't make excuses."
Kidd wore a protective vest to shield the rib.
"I don't feel discomfort," Kidd said. "The adrenaline a lot of times can carry you through. It's just in the morning that you feel it the most."
As for the passing of the trade deadline, Kidd said the Nets can now focus on trying to make the playoffs with the existing group.
"Each time we take the floor we've got to try and find a way to win," Kidd said. "Tonight was a good start for that."
Ron Artest had 33 to lead the Kings, who lost for the fifth time in their last six games.
"I always feel that you have to play like champions and I just think we aren't right now," Artest said.
The Nets led 19-11 after a sloppily played first quarter that saw each team turn the ball over eight times. The Kings shot poorly throughout the period, opening the game 2-for-15 from the field. Sacramento finished the quarter 5-for-20.
Williams, who came in late in the first period to spell Kidd, sparked New Jersey to a 15-8 run starting the second quarter to give the Nets a 34-19 lead. Williams scored six points in the surge.
Kidd replaced the rookie with 7:29 remaining in the half and kicked up the tempo that Williams established. Kidd scored 13 points and dished out six assists the rest of the way as the Nets took a 57-39 lead into the locker room.
The Kings had more turnovers, 14, than field goals in the half, 13. Artest led Sacramento at the half with 13 points.
The Nets cruised through the third quarter, leading by 27 at one point. Carter had 14 points in the period to help New Jersey lead 86-68 after three.
In the fourth, Sacramento finally mustered a run and managed to whittle the Nets lead to eight when Quincy Douby scored on a layup with 1:42 left. Williams sealed the win with a 3-pointer, on feed from Kidd, to put New Jersey up 105-94.
"New Jersey came out and really defended well," Kings coach Eric Musselman said. "They jumped out early. Our guys played hard in the second half, especially the group in the fourth quarter. They played until the final buzzer went off."
- This was the second of a four-game-in five-night road trip for the Kings. They dropped a 109-106 decision to the Wizards on Thursday. The Kings will play in Indiana on Sunday and at Philadelphia on Monday before heading home. Sacramento has lost four straight on the road.
- Kings forward Kenny Thomas left the game in the third quarter with a sprained jaw and did not return.
- The Nets are 4-7 in their last 11 games, holding their opponents under 100 points in all four victories.