Quentin Richardson, getting more playing time in the absence of small forward Jared Jeffries, added 15 points, including seven in the final quarter.
Coming off a 23-59 season, the Knicks (3-0) moved halfway to a perfect exhibition season - not to mention equaling the longest winning streak they had in 2005-06.
Jeffries, expected to be the starting small forward, is out six to eight weeks with a broken left wrist.
Wally Szczerbiak and Tony Allen each scored 18 points for the Celtics, who fell to 1-3.
The Celtics played without All-Star Paul Pierce, who missed his first game of the preseason because of a strained left hip.
Richardson's jumper snapped a 94-all tie with 6½ minutes to go and New York led the rest of the way. Boston was within two with under four minutes to play before Richardson scored and fed David Lee for a basket on consecutive possessions to make it 105-99 with 2:56 remaining.
Lee finished with 11 points and 12 rebounds.
The Knicks trailed by 12 points early in the second quarter before a 25-10 surge, sparked by Crawford's outside shooting and first-round pick Renaldo Balkman's energy, gave them a 53-50 lead with 2:01 left in the half. New York led 58-56 at halftime.
Balkman took a hard fall with 6:25 left in the second period, landing on the back of his head after Szczerbiak fouled him to prevent a fast-break dunk. But he shook it off and made one of the free throws.
Boston's Sebastian Telfair scored 14 points, all in the first half. The former high school star in Brooklyn and cousin of Knicks guard Stephon Marbury didn't play in the second half because he was feeling ill.