Anderson beat Djokovic 7-6 (7-5) 5-7 10-6, sending down 17 aces in the match to help him out of trouble.
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.
The win gives the World an 8-7 lead with three singles rubbers to be played later on Sunday.
This is the second instalment of the Laver Cup which has been dubbed the Ryder Cup of tennis - although it lacks the tradition of golf's premier team event. In the event of split sets, the third set is a 10-point match tiebreaker.
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Federer, speaking to ESPN on the sidelines of this weekend's Laver Cup, has skipped the clay-court segment of the season since 2017 in order to conserve energy for Wimbledon and hard-court seasons.
"It's pretty nice to play indoors - no sun, no wind", Dimitrov said.
Djokovic, who has won the last two Grand Slams to move to within six of Federer's record tally, missed the inaugural tournament a year ago due to an elbow injury.
"I'm just happy to get the win and we defended the title, that's the most important thing".
You might have heard of Bjorn Borg and John McEnroe, who have a combined 18 Grand Slam singles titles and a mountain of other tennis accolades.