Federer had to win a tense tie-break over world number 20 Isner to take the three points, smashing an ace on the final point to raise the roof in Geneva after the American had somehow shot wide with the court at his mercy.
Team World lead 11-10 ahead of German Alexander Zverev’s clash Milos Raonic, a straight shootout for the tournament after Taylor Fritz had earlier put Team World to within one win of capturing their first Laver Cup with a 7-5, 6-7 (3/7), 10-5 win over Dominic Thiem.
“I’m thrilled that I was able to give something back to the team,” said Federer.
“Obviously to see Rafa on the sidelines after having to pull out with an injury, it’s great camaraderie I feel.”
Team World came into the day 7-5 down but was boosted by Rafael Nadal’s withdrawal with a hand injury.
Fritz, himself a replacement for injured Nick Kyrgios, followed up on Isner and Jack Sock’s 5-7, 6-4, 10-8 defeat of Federer and Stefanos Tsitsipas with a surprise tie-break triumph over world number five Thiem.
“That was such a big match for Team World to win, we really needed that,” said Fritz.
“This has to be one of the biggest wins of my career. It means so much more when you’re playing for other people as well.”
This year is the first time the tournament has been played since being added to the ATP Tour.
Europe won the 2018 edition 13-8 in Chicago.