Harden scored 18 points in the fourth quarter to eclipse the 57 points Calvin Murphy scored in 1978 to break Houston's single-game scoring record. After Harden broke the record, cameras in the arena showed a shot of Murphy, who works on the television broadcast team, smiling and clapping for the Beard, who also had 10 rebounds and 11 assists.
The game was tied at 107 after a basket by Marreese Speights with just under four minutes to play. Neither team scored for more than two minutes after that before Harden took over, scoring the next six points to make it 113-107 with 45 seconds left.
He set the scoring mark when he stepped back and made a three-pointer before crashing to the court after being fouled by Mario Hezonja. He then made the free throw to give him 60 points and bringing the crowd to its feet.
Harden, who also had four steals and a block, grabbed his 10th rebounds a few seconds later to give him his third triple double this season. He made 17 of 18 free throws and was 19 of 30 from the floor with five three-pointers.
Hezonja and Speights scored 17 points each for the Magic, who dropped their third straight.
The Rockets started the game without Chris Paul, who has a sore groin, and Trevor Ariza, who is dealing with a strained hamstring. They lost another player when Eric Gordon, who is second on the team in scoring with 19.5 points a game, left early in the second quarter with lower back stiffness.
Harden's big night came as he played a season-high 46 minutes and 26 seconds with Houston missing so many players.
It was his fourth 50-point game this season and Tuesday's performance bested his previous career-high of 56 points set in November against Utah.
Orlando led by two points with about 9 1/2 minutes left before the Rockets used a 10-4 run to make it 101-97 with about seven minutes to go. Harden made two three-pointers in that stretch, and wowed the crowd on the second one that he came as the shot clock was about to expire and with Shelvin Mack right in his face.
Houston didn't lead for long though, as Speights was fouled while making a three-pointer and added the free throw to tie it seconds later.
The Magic had a two-point lead with about 5 1/2 minutes left before Houston used a 6-2 run, with all its points from Harden, to take a 107-105 lead with about four minutes left.
The Rockets were up by one early in the third quarter when Harden scored all of the team's points in a 6-2 spurt that made it 64-59. Harden capped that run with his first 3-pointer of the game after missing all seven tries in the first half.
Houston had pushed its lead to seven later in the third after scoring four quick points. But the Magic used a 7-2 run, highlighted by a three-pointer by Mario Hezonja, to get within 72-70 midway through the quarter.
The Magic tied it on a basket by Jonathon Simmons with about four minutes left in the third, but the Rockets used a 5-2 run to regain the lead, 83-80.
Speights made a three-pointer to put Orlando back on top with just under a minute remaining in the quarter, but Houston scored the last four points of the quarter to take a 90-88 lead into the fourth.
Harden found Luc Mbah a Moute for a layup for the first basket in that span and added a jump shot just before the shot clock expired for the other points.
Harden piled up 16 points in the first quarter and had 24 by halftime despite his early three-point shooting woes.
at Detroit 125, Cleveland 114: Andre Drummond had 21 points and 22 rebounds, and the short-handed Pistons beat Cleveland 125-114 after the Cavaliers lost Kevin Love to a potentially season-altering hand injury. Love exited in the first quarter with a broken left hand, and the Pistons took advantage of his absence, snapping an eight-game losing streak despite a roster that was depleted by their blockbuster trade for Blake Griffin.
Sacramento 114, at New Orleans 103: Zach Randolph scored 26 points and grabbed 12 rebounds, and the Kings beat the Pelicans 114-103. Kosta Koufos had 17 points and 17 rebounds for the Kings, who were able to exploit the absence of Pelicans All-Star center DeMarcus Cousins by getting double-doubles from both of their starting big men.
at Washington 102, Oklahoma City 96: Beginning what could be a significant stretch without All-Star point guard John Wall, the Wizards got 25 points from Otto Porter Jr., limited Russell Westbrook to 13 and beat the Thunder 102-96 to end the Oklahoma City’s eight-game winning streak. Bradley Beal had 21 points and nine assists for Washington, which announced about 7 1/2 hours before tipoff that Wall will have arthroscopic surgery on his left knee.
at Toronto 109, Minnesota 104: The Toronto Raptors stiffened up after a sloppy first half to extend their streak of home dominance over the Minnesota Timberwolves. DeMar DeRozan scored 23 points, Jonas Valanciunas had 18 points and 11 rebounds and the Raptors rallied from a 13-point deficit in to beat the Timberwolves.
at San Antonio 106, Denver 104: LaMarcus Aldridge had 30 points and the San Antonio Spurs escaped with a 106-104 victory over the Denver Nuggets. The Spurs had four players in double figures, including 18 points each from Kyle Anderson and Pau Gasol.
at New York 111, Brooklyn 95: Kristaps Porzingis scored 28 points, Enes Kanter had 20 points, 20 rebounds and five assists, and the Knicks completed a New York City sweep of the Brooklyn Nets with a 111-95 victory. The Knicks returned home from their longest road trip of the season in new uniforms but their same old dominance of the Nets, with their fourth victory in four tries this season.
at Utah 129, Golden State 99: Ricky Rubio scored 23 points and handed out 11 assists as the Utah Jazz stunned the Golden State Warriors 129-99. The loss ended a three-game winning streak for the Warriors, who had won seven of eight before facing the Jazz.