The Swiss star won 6-4 7-6(3) for Team Europe to cut the deficit to one point, with World up 11-10 heading into last match.
Federer’s teammate Alexander Zverev will next take on Milos Raonic with three points on offer, guaranteeing the winner secures the required 13 points for overall victory.
“He’s a great player, good guy, confident exactly the right amount,” Federer said of Zverev. “That’s what we need in a final in a match.
“All the matches have been so close. I’m sure this one is going to go to the wire too, but we’re ready to go.”
Team World Captain John McEnroe said: “Everybody’s pumped up and if you told me a week ago it was going to be 11-10, I’d have taken it.”
Europe is trying to win the Laver Cup for the third time following victories in Prague 2017 and Chicago 2018, while World is desperate to get hold of the trophy for the first time.
Federer knew the Laver Cup was on the line as he stepped out in front of 17,000 expectant fans, and the 20-time Grand Slam champion well and truly delivered.
Up against one of the biggest servers in the game, the Swiss was focused from the outset.
Quickly up 0-40 in the fifth game, Federer broke for a 3-2 lead with a forehand winner and was never troubled in seeing out the set.
Isner held on when the pressure came midway through the second set, firing down a second-serve ace on one break point as he took it to a tiebreaker.
With serve dominating and the margins desperately fine, Federer made the breakthrough with a return winner for 5-3 and served his way to victory.
“I’m very excited,” said Federer.
“What an atmosphere, what a match. I’m thrilled that I was able to give something back to the team. Obviously to see Rafa on the sidelines after having to pull out with an injury, it’s great camaraderie I feel.”