Nets star Irving -- who had bagged 50 points last week in a victory over Charlotte -- delivered another performance for the ages against an outclassed Magic at Orlando's Amway Center.
Irving's tour de force surpassed his previous career best of 57 points, set in 2015 while playing for the Cleveland Cavaliers in a victory over the San Antonio Spurs.
"I felt good," Irving said after his epic display. "It really is a testament to the way we've been gelling as a team -- us just giving each other confidence and doing the right things.
"When you can get 60 in the flow of the game and it doesn't seem forced, and you're not putting up a few too many bad shots, and you come to the bench and guys are supporting you, telling you to go after the record -- that makes the basketball worth it."
The 29-year-old Australian-born seven-time All-Star made 20-of-31 from the field, making eight of 12 attempts from outside the arc.
A career-high performance for Irving looked inevitable after an explosive first half from Brooklyn.
The Nets piled on 48 points in the first quarter alone before adding 38 in the second quarter to lead 86-56 at half-time.
Irving contributed 41 points in that devastating first half, leaving him only 16 shy of his individual record.
He brought up 50 points -- the sixth half-century of his career -- with a driving layup in the third quarter, prompting appreciative chants of "Kyrie, Kyrie" from the Orlando crowd.
Two free throws saw him reach his record at 57 and then a magical three-point pull-up from 26 feet saw him hit the 60-point mark.
The Suns downed the New Orleans Pelicans 131-115 to extend their lead at the top of the Western Conference, with Devin Booker scoring 27 points.
The Heat meanwhile downed the Detroit Pistons 105-98.
Tyler Herro led the Miami scoring with 29 points, but the Heat were given an injury scare when Jimmy Butler hobbled off with an ankle injury.
In the night's other game, the Memphis Grizzlies romped past the Indiana Pacers 135-102.