David Lee added a season-high 20 points, teaming with Curry to wear out the Grizzlies' frontcourt. Curry, who had his career-best seventh straight game with 20 or more points, grabbed 15 rebounds before fouling out, and the Knicks shot a season-best 56.3 percent from the field.
Quentin Richardson also had 20 points and Stephon Marbury finished with 16 points and six assists.
The Knicks snapped a four-game losing streak at Madison Square Garden, where they are 2-7. Coach Isiah Thomas said his team's home woes were mental, with players worried too much about boos from the home fans.