Incredibly, Federer and Djokovic - with 34 grand slam titles between them - suffered Team Europe's only loss in Chicago.
The two stars, who share a great camaraderie on and off the tennis courts, seemed to enjoying playing together.
It took just three games for Federer to break the Australian in the opening set, but he waited for a shorter period in the second, breaking him at love in his first service game with a masterful combination of play that sent the capacity crowd to rapture.
Djokovic put his head in his hands as soon as his shot struck Federer in the back, and had an embarrassed look on his face.
Then, in a repeat of the Wimbledon final, Kevin Anderson, the runner-up in July, caused one of the biggest upsets of the tournament so far, beating Novak Djokovic 7-6 (7/5) 5-7 10-6.
Team Europe fared slightly better overall for the whole day, winning all of the opening singles' matches and ending day one with a 3-1 lead over Team World.
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This is the second installment of the Laver Cup, which has been dubbed the Ryder Cup of tennis although it lacks the tradition of golf's premier team event.
However, Anderson and Team World trail Team Europe 7-5 going into the final day of the three-day exhibition event.
World number two Roger Federer was barely ruffled as he cruised to a 6-3, 6-2 win over Kyrgios.
After the game, the duo sat on the bench during the break and had a light time discussing the moment and Federer was quick to say that this is why they don't play doubles as both laughed it off.
Europe had earlier built their advantage on singles victories for Bulgarian Grigor Dimitrov, Briton Kyle Edmund and Belgian David Goffin.
Novak Djokovic is a fun man and he is known for keeping it simple and enjoying his time on the court and on Saturday, he pulled off the ideal "fun" moment during a Laver Cup tie in Chicago.