However, Anderson and Team World trail Team Europe 7-5 going into the final day of the three-day exhibition event.
Britain's Kyle Edmund, a Laver Cup debutant, claimed an impressive 6-4 5-7 10-6 win over Sock and match three saw Belgium's David Goffin add to Europe's advantage as he beat Argentina's Diego Schwartzman 6-4 4-6 11-9.
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.
"It's not easy playing one of the best players of all time, but what an unbelievable atmosphere".
Under the scoring system for the Laver Cup, victories on day two are worth two points each, with victories on day three rising to three points.
Defending champion Europe needs 13 points to take the title, which is being held for the second time.
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The current World No. 21 steadied to shoot par on 17 and then sank a two-footer for birdie on 18 to tie his English rival. Rory McIlroy , victor of the event two years ago, signed for a 68 and is in third place two shots back at five-under par.
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Jack Sock and Kevin Anderson combined to deliver the sole triumph for their side, overcoming the world's second and third ranked singles players 6-7 (5) 6-3 (10-6) to prevent an opening day shutout for Team Europe. Dimitrov rolled through the opener with a 6-1 6-4 victory over American Frances Tiafoe before his team mates were required to dig deeper for their wins.
Anderson closed it out when the Serb fired a forehand into the net and the South African was mobbed by his teammates. "It was absolutely awesome".
"I felt good from the beginning and that's not usual", Federer said afterwards.
It wouldn't be a Kyrgios match without a bit of drama with the officials - and there was even more fireworks with Team World captain John McEnroe on the scene.
Federer and Djokovic eventually lost the match 7-6, 3-6, (10-6).
Zverev then raced into the lead in the tiebreak before closing out for the win.