Jalen Brunson scored 20 points as the Knicks romped to a 54-point margin of victory, eclipsing their previous biggest winning margin of 48, achieved in 1968, 1972 and 1994.
The victory over their New York rivals at Madison Square Garden followed a dismal run of four straight losses that culminated with a 114-97 drubbing by Dallas on Monday.
Knicks coach Mike Brown's frustration had boiled over following that loss, and he revealed later he had challenged his team to "do your job" in a half-time dressing down after they conceded 75 points in the first half alone.
Brown's message appeared to have hit home on Wednesday as his team roared into a 38-20 lead after the first quarter before accelerating away, at one stage leading by 59 points.
"Just seeing us play the way we're capable of playing, to go see them put it together for 48 minutes was a lot of fun," Brown said after the rout.
Brunson said the win was a stepping stone as the Knicks approach the midpoint of the season in third place in the Eastern Conference, behind the Detroit Pistons and Boston Celtics.
"We just had to refocus and get back to who we are," Brunson said.
"This is a good step for us, but we've got to continue to press the issue of getting better every single day."
In the Western Conference, Shai Gilgeous-Alexander kept his incredible scoring streak alive with 40 points as the reigning NBA champions Oklahoma City Thunder cruised to a 122-102 road victory over the Milwaukee Bucks.
Gilgeous-Alexander has now scored 20 points or more in 115 consecutive games, leaving him just 11 adrift of Wilt Chamberlain's record of 126 20-point games set between 1961 and 1963.
Oklahoma City improved to 37-8 with the victory and now lead the Western Conference from the San Antonio Spurs, who are second on 30-14.
"We have a bunch of guys that are driven and hungry, but not satisfied with one championship," Gilgeous-Alexander said.
"We play this game to be great and maximise our potential and we still feel like we have a lot of room to grow and that's what we're chasing."
Also on Wednesday, the Detroit Pistons extended their winning streak to four games with a wire-to-wire 112-104 defeat of the New Orleans Pelicans on the road.
Jalen Duren scored 20 points for Detroit as the Pistons maintained their comfortable lead at the top ahead of the second-placed Boston Celtics, who were 119-104 victors over the Indiana Pacers.