New York won its sixth in a row after building a 69-41 advantage at intermission.
Memphis closed within five points with 34 seconds left when Tony Allen made two free throws.
Raymond Felton then hit 1-of-2 foul shots for the Knicks and he grabbed his own rebound when he missed the second attempt. That led to Smith going to the foul line and his two shots boosted the New York lead to seven with 26 seconds remaining.
Smith scored 35 points and hit 10-of-18 from the field as part of New York's 51 percent shooting effort.
Carmelo Anthony added 22 points for the Knicks while Iman Shumpert had 16 and Felton contributed 13.
Memphis, which lost for the third time in four games, was led by 26 points from Mike Conley.