Smith went 9-of-10 from the free throw line and Raymond Felton connected on 8-of-12 shots from the field en route to 19 points for the Knicks, who recorded their only win of a five-game road trip.
Chris Copeland, filling in for the injured Carmelo Anthony (knee), contributed 14 points and six rebounds in the victory.
Kenyon Martin provided nine points and nine boards for New York.
Gordon Hayward led Utah with 17 points and four blocks.
Al Jefferson logged a double-double of 10 points and 11 rebounds in the loss.