Woodson started Stoudemire and Smith in the second half and the Knicks opened the third with a 15-3 spurt, catching the Cavs at 64-all.
The Cavs were without rookie starters Dion Waiters and Tyler Zeller, who were both stricken with a nasty stomach virus over the weekend. They were taken to the hospital to get fluids, but were resting at home during the game.
Cleveland's Marreese Speights made his first 10 shots and finished with 23 points. Luke Walton added a career-high 12 assists for the Cavs, who hadn't lost at home to the Knicks since 2006.
Despite shooting 4 of 18 from the field, the Cavs carried a 74-70 lead into the fourth.
However, the Knicks erased that with three quick 3-pointers, the last by Novak to make it 79-78 with 9:09 remaining. Kidd also made a big 3-pointer with 1:36 left put the Knicks up 97-91.
Irving picked up a quick assist and then made his first shot — a 3-pointer — and set the early tone for the Cavaliers, who shot 74 percent (14 of 19) in the first quarter and opened a 10-point lead.
NOTES: Anthony had six points and three turnovers before he got hurt. ... Knicks C Marcus Camby played for the first time since Jan. 10. He had been sidelined with plantar fasciitis. ... Former Knicks sartorial star Walt "Clyde" Frazier received a nice ovation when he was shown on the arena's scoreboard. Frazier played 66 games for Cleveland in the 1970s after he was traded by New York. ... According to Forbes, Cavs owner Dan Gilbert is worth $3.5 billion. In the magazine's annual ranking of the world's billionaires, Gilbert is 348th. He has added more than $1.5 billion to his net worth since September — and $2 billion over the last year. Gilbert controls about 40 companies.