Rune is part of the European team in the tournament, where Europe competes against the rest of the world.
With Rune's defeat, Europe fell behind by 3-5 to the rest of the world. It takes 13 points to win the tournament.
Rune was also on the losing side in his doubles match as Alex de Minaur and Alex Michelsen completed the Saturday sweep for Team World with a 6-3, 6-4 win against Holger Rune and Casper Ruud, stretching the lead to 9-3.
All four of Team World's wins on the day came in straight sets. With Sunday's four matches worth three points apiece, Team World needs just two more wins to take back the Laver Cup.
De Minaur and Michelsen took an early lead by breaking Ruud’s serve, sealing the opening set. The moment of the night came when De Minaur caught his own racquet on his ear while blocking a bullet from Rune. De Minaur required a medical timeout, yet somehow still won the point.
It's still uncertain if Rune will be in action on the last day of the tournament.