Kris Joseph's consecutive three-point plays to open the fourth quarter, part of a 24-4 stretch, gave Boston its first lead since the 7:34 mark of the first quarter.
Jason Terry added 22 points for the Celtics (3-4), who rested Kevin Garnett and Paul Pierce.
Rookie Chris Copeland scored 34 points and James White added 16 for the Knicks (2-2), who edged Boston last week in Hartford, Conn. but won't see the Celtics again until Jan. 7.
The Knicks led 52-47 at halftime.
A night after losing to Toronto in Montreal, the Knicks rested their starting frontcourt of Carmelo Anthony, Amare Stoudemire and Tyson Chandler.
They stay in upstate New York to play Philadelphia on Monday in Syracuse, sending Anthony back to where he won a national championship in 2003 as a freshman, an NCAA tournament run that included a stop here.