Langston Galloway contributed 13 points for the Knicks, who have won two of their last three.
New York had eight players score at least six points.
Carlos Boozer had 19 points with 10 rebounds and Jordan Clarkson added 19 points in the loss.
Los Angeles has lost 11 of its last 12 games on the road.
"We just got off to a bad start in the first quarter," Lakers coach Byron Scott said.
Jason Smith led an efficient offense for the Knicks in the first quarter with nine points. New York shot 56 from the floor and limited Los Angeles to just 5-of-20 shooting over the first 12 minutes, taking a 32-19 lead into the second.
Neither team shot particularly well in the second quarter, with the Lakers again shooting under 30 percent in the frame. They did, however, manage to cut the deficit to 47-39 at the break.
Anthony scored New York's final 12 points of the third as it led 72-57 entering the fourth.
The Knicks led by as many as 21 in the final period.
Lou Amundson pulled 13 rebounds in the win ... The Lakers were held to 35.5 percent shooting ... Wesley Johnson came off the LA bench and scored 11.