Despite their status as greats of the game, the US duo of Jack Sock and South Africa's Kevin Anderson pulled off a thrilling 6-7 6-3 10-6 win, with the match likely to be remembered for this unfortunate moment as Djokovic smashed a ball into his illustrious partner.
Despite the occasional flash of brilliance from Kyrgios, he was no match for Federer in the first set as the Swiss champion barely broke sweat to take it 6-3 after just 32 minutes.
"Obviously it's my debut this year but I was watching it on TV last year and it was very exciting to see a new concept".
Considering the Bulls were 27-55 last season, it's not as though Federer and Kyrgios could make things that much worse.
Chicago - John Isner and Jack Sock saved two match points before snatching a thrilling doubles victory over Roger Federer and Alexander Zverev as the World Team took a one-point lead over Europe at the Laver Cup on Sunday.
Federer and Djokovic didn't have quite the same buzzing chemistry like Federer had with Rafael Nadal a year ago.
Roger Federer and Novak Djokovic failed to make the scoreline 4-0 in Team Europe's favour
The next Laver Cup, which is named after Australian legend Rod Laver, will be staged in Geneva in September 2019. The winning team must reach 13 points.
"Kevin was so well prepared for this, we needed this bad", said World captain John McEnroe.
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.
The duo won the tie-breaker 10-6 and the match 6-7 (5) 6-3 10-6 to earn the first point for Team World. If the players split sets, they go straight to a 10-point tiebreaker.
Play resumes today with the tournament's final four matches worth three points apiece with everything to play for.
Djokovic, victor of the past two grand slam titles, double-faulted on set point to give the South African the advantage.