Harden finished 17 of 38 from the floor. He was only 5 of 20 on 3-pointers but was 22 of 25 from the line and grabbed 15 rebounds.
Carmelo Anthony holds the overall record at the current MSG with 62 points.
Rookie Allonzo Trier scored a season-high 31 points for the Knicks, who lost their seventh straight game. They lost coach David Fizdale when he picked up his second technical foul and was ejected with 1:08 remaining.
The Rockets led by 10 after three, but the Knicks quickly cut into it when Harden was on the bench. New York eventually took a couple late leads but couldn’t hold on, losing for the 15th time in 16 games.
Harden had already surpassed his average of 35.7 points by halftime, putting back the miss of his own shot to beat the buzzer and give himself 36 points and nine rebounds.
Chamberlain still has all three 30-point streaks that were longer. His record is 65 straight, and he also had streaks of 31 and 25 games.
Rockets: Chris Paul appears close to returning from a left hamstring strain. Coach Mike D’Antoni said it could be by the end of this week, with the Rockets next playing Friday at home against Toronto. If not, D’Antoni said it could be early next week.
Knicks: Fizdale said Luke Kornet’s sprained left ankle could have been much worse, but that the center would still miss at least a couple weeks.
Rockets: Host Toronto on Friday.
Knicks: Visit Brooklyn on Friday.