New York was also without starting point guard Raymond Felton, who has a broken left pinkie finger and is expected to miss at least a month.
Cousins was back in the starting lineup after missing the previous two games after Sacramento suspended him for unprofessional behavior and conduct detrimental to the team after a verbal confrontation with Smart during a game Dec. 21 against the Clippers.
"I wanted to get this thing behind us, get it over and move on," said Smart, explaining his decision to put Cousins back in the starting lineup. "He was rusty, yes. But he made some big plays down the stretch."
Chandler dunked on an alley-oop pass from Kidd midway through the third quarter. The next time down the court, Kidd stepped back for a 3-pointer, giving the Knicks a 97-95 lead, their first lead since the opening minutes.
Smith scored 11 points in the third quarter when the Knicks used a hustling defensive effort to outscore the Kings 31-16 and pull to 87-81 heading into the fourth.
Following a lethargic first half, the Knicks showed much more energy in cutting into Sacramento's 21-point halftime lead. Back-to-back three-point plays by Smith and Chandler trimmed the Kings lead to 85-77 with 2:17 left in the third.
Thornton scored 11 first-quarter points to help the Kings take an 11-point lead into the second. Fredette took over the offensive load in the second quarter, making three 3-pointers and scoring 15 points, helping the Kings to a 71-50 lead at the half.
"We buried ourselves in the first two quarters, then we decided to defend in the third and fourth quarter," Woodson said. "We got back in it and had control at the end. They made a great shot."
Copeland and Smith had 13 points in the first half for the Knicks, who trailed 68-41 late in the second quarter.
The Knicks poor perimeter defense in the opening half cost them repeatedly with the Kings making 10-of-15 attempts and producing a season high for points in one half. Sacramento shot nearly 60 percent overall and had 19 assists, another season-high for a half.
NOTES: In the first quarter, the Kings connected on four straight 3s in four possessions, building their lead to 26-14. ... Woodson was a starting guard for the inaugural Sacramento team that relocated from Kansas City for the 1985-86 season. ... Kings starting guard Tyreke Evans has missed six straight games and 11 of the last 15 due to an injured left knee. He may try to play Sunday against Boston. ... Knicks reserve forward Rasheed Wallace was out with a sore left foot. ... The Knicks are hoping injured forward Amar'e Stoudemire will return sometime next week. A knee injury has kept Stoudemire inactive all season.