Federer, this year's Australian Open and Wimbledon champion, won 4-6, 7-6 (8/6), 11/9 to give Team Europe an unbeatable 15-9 lead yesterday.
But the 36-year-old Swiss legend struggled against the 20th-ranked, 22-year-old Australian and his flawless serve, losing the first set on a single break.
When he finally broke Kyrgios halfway through set two, he yelled "Come on!" in relief, only to lose his serve again in the next game.
But Federer capitalised on the system of the tournament he had founded -- forcing Kyrgios into longer exchanges, he edged him in the second-set tie-break, then came back from 8-5 down in the decisive super tie-break.
"It was a nail-biter at the end but for me personally it was a dream scenario."
"It was an incredible journey really, it was way better than I ever thought it would be," he added about the tournament.
"It felt like winning some of the biggest matches in my life. It was like a fairy tale."
Kyrgios said the loss "just hurt."
"I gave everything I had and I came short."
The start of the clash saw the controversial Kyrgios briefly kneel on the court in a gesture which sparked speculation that he was joining the ongoing protest against US President Donald Trump.
A host of NFL players chose to kneel in games across the US on Sunday during the playing of American national anthem in a demonstration against racial inequality.
- 'Lucky' -
===========
Team Europe, the odds-on favourites with five of the world's top seven players, entered Sunday with a 9-3 lead which narrowed as Jack Sock and John Isner beat Tomas Berdych and Marin Cilic in the opening doubles rubber.
On Sunday, the winner of each rubber earned three points, against one on Friday and two on Saturday.
Sock and Isner beat Berdych and Cilic 7-6 (7/5), 7-6 (8/6) with Sock's vicious forehand leading the charge on the American's 25th birthday.
In the day's second rubber, a break in each set was all German youngster Zverev, the world number four, needed to beat 16th-ranked American Querrey 6-4, 6-4 in their first-ever encounter.
Isner's greatest moment was yet to come as the world number 17 edged Nadal, this year's French and US Open champion.
He then swept Nadal in the second-set tie-break after both held on to their serves.
"We were lucky to be 9-3 before today," said Nadal. "We are very happy to win the first Laver Cup for Europe. Let's enjoy this moment."
Skippered by Bjorn Borg, Team Europe also comprised Dominic Thiem, while Frances Tiafoe and Denis Shapovalov played for John McEnroe's Team World earlier in the tournament.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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