The Knicks learned before the game their point guard would likely be lost for the season with a torn meniscus in his left knee. They are also missing forward Amar'e Stoudemire, who is out 2-4 weeks with a bulging disk in his back.
But Smith responded with nine rebounds and five steals, while Tyson Chandler recorded 14 points and 12 rebounds as New York won for the fourth time in five games.
The Knicks came into the contest clinging to the eighth and final playoff spot in the Eastern Conference.
Antawn Jamison could not prevent the Cavaliers' seventh straight loss despite 13 points and seven assists.