Nick Kyrgios had overcome a 0-4 deficit in the first-set tie-break to take the opening set in Geneva, Switzerland.
But Federer fought back from two games down in the match tie-break to defeat the Greek 7-6 (7-5) 5-7 10-7.
Federer maintained his unbeaten run in Laver Cup singles matches with a 5-0 record.
Kyrgios won a spectacular 31-stroke rally with a backhand winner early in the game which saw him claim the opening set, but a weak service game from the Greek at 5-5 in the second set gave the world number three the advantage.
“It was really close that first set so it was tough to lose,” Federer said. “The crowd could feel it, I could feel it.
“I needed to get some energy going but you can’t do that if you don’t play any good shots and Nick was playing very well.
“I was just trying to stay focused. If you can turn the momentum, the crowd gets back into it and I need some earplugs next time, it was just phenomenal.”
Earlier, American Isner temporarily gave Team World a lifeline by defeating Alexander Zverev 6-7 (2-7) 6-4 10-1.
The 34-year-old was two games from defeat but overcame the German, with the overall score standing at 3-3 prior to Federer and Kyrgios taking to the court.
“Maybe we’re turning the tables just a little bit,” Isner said. “Team World is in this and we’re here to win, so let’s get it going!”
A first-set tie-break saw world number six Zverev beat the American 7-2. In the second set, the score was tied at 4-4 when Isner broke Zverev’s serve, going on to win the set 6-4.
But a match-deciding tie-break saw world number 20 Isner win seven points before Zverev was able to get a point on the board, his only point in a 10-1 tie-break.
Later on Saturday, Rafael Nadal will play his first matches of the weekend when he faces Milos Raonic in the singles, before teaming up with Stefanos Tsitsipas to face Kyrgios and Jack Sock in the doubles.
Day two of the three-day tournament awards two points per win, with the first team to reach 13 points declared the winner.
The Laver Cup is into its third year but this is the first time the tournament is an officially sanctioned ATP Tour event.
The previous tournaments in Prague and Chicago took place on an exhibition basis.