Reserves Fred Jones and David Lee stepped into the lineup and both finished in double figures, helping New York beat its cross-river rival for only the second time in the last 12 regular-season meetings.
Kidd missed a game for the first time this season because of a migraine, and the Nets -- already one of the NBA's poorest offensive teams -- failed to get anything going until they already trailed by 14 in the fourth quarter.
"I thought overall it was still a great victory for us," Lee said. "Both teams were missing key players and we were able to come out on top, and any time you come into this place and get a victory it's huge.
"With stuff on the court and off, we haven't had the best week. But this is a very positive thing today, coming in here a little bit short-handed and coming out with a victory on the road."
"They were short-handed, too," Jefferson said. "We had more than enough out there on the court to win. I've been standing by that even when we were missing a couple of guys. Jamal Crawford played well. Zach Randolph took advantage of getting some extra touches. It made it tough."
New York got its first road win in eight tries this season. The Nets fell to 20-5 in the regular season against the Knicks since acquiring Kidd in 2001. New Jersey also swept a four-game series in the first round of the 2004 playoffs.
"I guess we were due," Knicks coach Isiah Thomas said.
Marbury's father died Sunday night during the Knicks' home loss to Phoenix. The funeral is Thursday, but Thomas had left open the possibility earlier Wednesday that his point guard could travel to New Jersey for the game.
Marbury sent a statement during the game, thanking fans for their "outpouring of support, heartfelt prayers and words of encouragement."
Curry sprained his left ankle at the morning shootaround, leaving the Knicks without two of their top four scorers. But Jones and Lee did their part, finishing with 15 and 13 points.
"We said that we thought we had capable people in the locker room who would step up and they were capable of playing," Thomas said, "and those two guys did an excellent job just in staying within themselves and doing what they were capable of doing."
Crawford and Nate Robinson hit 3-pointers to open the fourth quarter, pushing New York's lead to 80-66. The Nets answered with nine straight points, including a pair of 3s from Nachbar, to get within five, but Randolph scored inside, Jones scored four in a row, and the Knicks were safely ahead again at 86-75.
New Jersey made a final push, cutting the lead to 90-85 on Jefferson's three-point play at the 2-minute mark. Crawford then hit a long 3 as the shot clock was winding down.
Without Kidd, and with reserve point guards Marcus Williams and Darrell Armstrong still out with injuries, the Nets had nobody to run the offense. Eddie Gill, a call-up from the NBA Development League, started for Kidd and fouled out with four points and four assists.
Randolph made all four shots from the field and scored 10 points in the first quarter, when the Knicks led by as many as 10 before settling for a 26-18 lead. The Nets shot only 5-of-17 (29 percent) in the second period, preventing them from making up any ground. New York led 51-42 at halftime.
The Nets were also without swingman Antoine Wright, who has a sore left shoulder.
Carter had an MRI Wednesday morning after briefly leaving Tuesday's game with an injury to his lower right leg. Nets coach Lawrence Frank said Carter had discomfort in the area between his calf and Achilles' tendon, but the MRI was negative. ... Thomas said the Knicks would attend Donald Marbury's funeral in Brooklyn. There was a moment of silence for Marbury before the game. Stephon Marbury also played for the Nets, before he was traded to Phoenix in the deal for Kidd in the summer of 2001. "My father left his legacy [where] he always wanted us to finish playing, at MADISON SQUARE GARDEN...," Marbury said in his statement.