The result meant Team Europe were locked at 2-2 with Team World at the end of the opening day of the Ryder Cup-style event.
“We’ll get through this somehow, will we? Right?” Federer said with a cracked voice.
“I’m happy, I’m not sad. It feels great to be here and I enjoyed tying my shoes one more time. Everything was the last time. The match was great, I couldn’t be happier. It’s been wonderful.”
Federer has enjoyed a storied rivalry with Spain’s Nadal over nearly two decades — together they have won 42 Grand Slam singles titles in a golden era for the men’s game.
The pair, who first met in 2004, played 40 times, including in nine Grand Slam finals, with Nadal holding a 24-16 winning record.
But in a match that started late Friday they were on the same side of the net in a fitting farewell for Federer, who turned professional nearly a quarter of a century ago.
There was a huge roar and standing ovation as the Swiss great and Nadal came onto the black court, dressed in blue shirts and white shorts, both wearing white headbands.
Both teams held serve fairly comfortably at the start of the match, with cries of “Let’s Go Roger, Let’s Go” breaking out at 3-3.
But Federer and Nadal seized on their first break point in the 10th game, winning the first set when Sock netted with a backhand to huge cheers.
The American pair levelled the match by taking the second set tie-break with ease.
In a nerve-shredding match tie-break, Federer was unable to serve out for the match at 9-8, with the Americans winning the next three points to emerge victorious.
The Swiss was overcome with emotion afterwards, hugging teammate Nadal and waving to the crowd.
He was unable to contain his emotion when addressing the arena during his on-court interview, breaking down in tears.
“Playing with Rafa on the same team, and having the guys, everybody here, all the legends… thank you,” said Federer, who was joined on court by his parents, wife Mirka and their four children.
“It does feel like a celebration to me,” he added. “I wanted to feel like this at the end and it is exactly what I hoped for so thank you. It has been a perfect journey and I would do it all over again.”
The six-strong Team Europe also includes Novak Djokovic and Andy Murray — the other two members of the so-called “Big Four”, who have dominated the men’s game for so many years.
Italy’s Matteo Berrettini will take Federer’s place over the weekend as an alternate, with the Swiss great opting out of singles matches.
Europe have won all four previous editions of the Laver Cup and took a 2-0 lead after the opening session in London, courtesy of wins for Norway’s Casper Ruud and Greece’s Stefanos Tsitsipas.
Tsitsipas shrugged off a dramatic on-court protest by a demonstrator who set his own arm ablaze to protest the use of private jets to beat Argentina’s Diego Schwartzman 6-2, 6-1.
In the evening session Murray lost a gruelling encounter to De Minaur 5-7, 6-3, 10-7 before all eyes turned to Federer.
The Swiss is leaving the stage 19 years after winning his first Grand Slam title at Wimbledon in 2003.
He retires with a men’s record of eight Wimbledon crowns, 103 titles overall and more than $130 million in prize money alone, won with a game defined by a rare elegance and precision.
Nadal (22) and Djokovic (21) have both surpassed Federer’s tally of Grand Slam titles but Team World captain John McEnroe said Federer’s retirement would leave “a void that will never be filled”.
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