With 169 singles titles between them, and a combined total of 34 career Grand Slams, both are sure to go down in history. Djokovic covered his mouth with his left hand and leaned over after the ball went off his partner.
Day Two will feature three more singles clashes, including Federer v Nick Kyrgios, and an additional doubles match, with two points on offer for any victory.
The current Wimbledon and US Open champion was quick to see the amusing side, however, and immediately rushed to Federer's aid before giving him a hearty rub on the back to make amends.
During the contest, Djokovic accidentally smashed a forehand into Federer's lower back, much to the amusement of the crowd.
The second set was a similarly cagey affair, going with serve for the first ten games - then Sock broke Edmund, who was playing his first match since his US Open defeat to Paolo Lorenzi, and held his own to take it 7-5 and force a third-set tie-break.
David Goffin edged Diego Schwartzman 6-4, 4-6, 11-9; Kyle Edmund beat Sock 6-4, 5-7, 10-6; and Grigor Dimitrov downed Frances Tiafoe 6-1, 6-4.
The exhibition is taking place on United States soil for the first time and features 12 of the world's top players squaring off against each other in a three-day showcase which wraps up Sunday in Chicago. Federer said to Djokovic during a break between games.
Schwartzman and Isner will be representing Team World in the second instalment of the Laver Cup from Chicago this weekend.
Federer and Djokovic last played against each other in the Cincinnati final on August 19, when Djokovic won 6-4, 6-4 to become the first player to claim all nine ATP Masters 1000 events since the series started in 1990.