Anderson drained seven 3-pointers and Tyreke Evans added 24 points with seven assists as New Orleans corralled a fifth victory in seven games.
But the triumph was overshadowed by the loss of Davis to a non-displaced fracture in his left hand, suffered during the first quarter.
No timetable for the former No. 1 overall pick's return to action was immediately announced. He was averaging 19.6 points, 10.6 rebounds and a 3.9 blocks per game.
Jrue Holiday had 11 points and nine assists for the Pelicans.
The Knicks dropped a ninth straight despite 23 points and 10 rebounds from Carmelo Anthony.
Tim Hardaway Jr. added a career-high 21 points.