The Knicks led by 20 points heading into the final period and improved to 3-2 since the trade that brought Anthony to the New York from Denver.
Stoudemire and Douglas both scored 24 points and Anthony had 22 as part of a 54-percent shooting effort by the Knicks. Douglas started at point guard in place of Chauncey Billups, who also came from Denver in the blockbuster trade and who missed the game with a bruised left thigh.
The Hornets were led by 21 points off the bench from Jarrett Jack.
New Orleans lost its third straight, the last two coming at the start of a five-game road trip, and has gone 4-12 since reeling off a 10-game winning streak in January.