Harden eclipsed his previous career-best of 46, set in 2013, on a free throw with about a minute remaining. On Houston's next possession, Trevor Ariza found him in the corner and he swished a three-pointer under heavy pressure, to make it 50.
Six straight points by the Nuggets cut the lead to eight with about five minutes left when the Rockets made the next five points, capped by a step-back jump shot from Harden, to make it 104-91. Harden scored seven points after that to secure the victory.
It was the 29th game with at least 30 points and seventh with 40 this season for Harden, who entered the game second in NBA scoring. He bounced back from a tough shooting game on Tuesday, where he had 17 points, by scoring 22 before halftime on Thursday night.
Houston made 32 free throws in the game, led by 22 by Harden, which were the most made by a player in the NBA this season.
Wilson Chandler and Randy Foye scored 23 points each for the Nuggets, who dropped to 0-4 against Houston this season.
The Rockets led by 17 after three, but with Harden on the bench, the Nuggets used an 11-2 run to open the fourth quarter and get within 92-84 with 8 1/2 minutes left.
Houston's star came in and helped the Rockets go on a 7-1 run to extend the lead to 99-85 midway through the quarter.
Minnesota 95, at New York 92 (OT): Zach LaVine made the tying and go-ahead free throws with 10.7 seconds left and scored six of his 20 points in overtime as the Timberwolves outlasted the Knicks in a matchup of the NBA's biggest losers. Minnesota (15-53) ended a six-game losing streak and snapped a tie with the Knicks (14-54) for the NBA's worst record. New York can still win for losing, and now has pole position in the race for the No. 1 draft pick. Kevin Martin scored 22 points and Andrew Wiggins had 20 for Minnesota despite shooting four for 17 from the field.
at Phoenix 74, New Orleans 72: Brandan Wright scored 16 points and matched his career high with seven blocked shots for the Suns, who won despite their cold shooting. The Pelicans played without star Anthony Davis, who had rolled his left ankle in the team's shootaround earlier in the day. His availability for today's game at Golden State was uncertain.