New York led by 18 with 7:25 to go only to have the Clippers pull within one with a 21-4 run.
Smith's jumper ended the charge and he added two free throws to give the Knicks their second straight win.
New York is tied with Philadelphia for the No. 7 seed in the Eastern Conference going into Thursday's final regular-season games. The Knicks own the tiebreaker over the 76ers and will finish in the seventh spot with a win over Charlotte or a Philadelphia loss to Detroit.
The Clippers closed out their regular campaign and dropped a half game behind Memphis for the fourth seed in the West. Los Angeles and Memphis will meet in the opening round of the playoffs, but the host team for the series opener has yet to be determined.
A win by Memphis Thursday over Orlando would give the Grizzlies home-court advantage over the Clippers. If Orlando defeats Memphis, the Clippers will be at home for the first two games of the series.
Blake Griffin paced the Clippers with 29 points and 10 rebounds.