Carmelo Anthony scored 21 to lead the Knicks, who have won three of their last four. It was New York's first victory since returning from a trip to London, where the Knicks defeated Detroit last week.
Smith's 3-pointer gave New York a five-point lead and Boston could manage only a single field goal from Rajon Rondo the rest of the way while turning the ball over twice.
The Celtics have lost five in a row to drop two games below the breakeven mark.
Anthony hit just 11-of-28 shots and the Knicks went only 38 percent from the field. Amar'e Stoudemire added 15 points and nine rebounds off the bench for New York and Jason Kidd had 12 points.
New York overcame a triple-double from Rondo, who scored 23 points, grabbed 10 rebounds and handed out 11 assists. Paul Pierce had 22 points.