Zverev showed immense composure to close out a 6-4 3-6 10-4 victory and hand Bjorn Borg’s team a 13-11 overall win.
Alexander Zverev snatched the Laver Cup for Team Europe as he beat Canada's Milos Raonic in the final rubber of a thrilling three days of action in Geneva's Palexpo Arena on Sunday.
With Roger Federer and Rafa Nadal, winners of 39 Grand Slam titles between them, part of the supporting bench, Zverev showed immense composure to close out a 6-4 3-6 10-4 victory and hand Bjorn Borg's team a 13-11 overall win.
With Nadal forced out with a hand injury at the start of the day and Federer suffering a doubles defeat, it looked as though John McEnroe's Team World would claim the title for the first time since the event began in 2017.
But after Federer defeated John Isner to close the gap, Germany's Zverev produced a flurry of superb backhands to beat the big-serving Raonic in the final rubber of the weekend.
After crunching a forehand winner, most of the 17,000 sell-out crowd erupted and Zverev was buried under his team mates with Federer, Nadal, Dominic Thiem, Stefanos Tsitsipas and Fabio Fognini celebrating a third successive victory for Europe.
It had been very tight though with the World Team leading 11-7 in the middle of the afternoon.
With three points for each rubber won on Sunday, McEnroe's team made a great start with Jack Sock and Isner beating Federer and Tsitsipas on the charcoal-coloured court.
American Taylor Fritz, in for the injured Nick Kyrgios, then extended his team's lead by beating Dominic Thiem 7-5 6-7(3) 10-5.
It meant that if Federer lost to Isner, Team World would win the title.
But with the Swiss crowd roaring his every winner, Federer preserved his 100% singles record in the event by claiming a 6-4 7-6(3) win before settling down at courtside to offer high-calibre vocal support to Zverev.
After Raonic battled back to level the match and set up a match tiebreak decider, Zverev left the court with Federer and Nadal in hot pursuit.
Their words of wisdom paid handsome dividends as Zverev fed off the energy from the crowd to play a superb tiebreaker.
"Team World came once again very close but we won the right points and had maybe a little bit of luck," Swede Borg said.
"I'm very proud of my team, they did a hell of a job. I'm a very happy captain."
American McEnroe looked crestfallen in defeat but congratulated his old adversary Borg.
"I'm getting very sick and tired of you," the American great told Team Europe after suffering his third successive defeat by Borg's men. "I'm so proud to be the captain of this team, they fought their hearts out. World, you guys are awesome."
Federer, who won his two singles matches over the weekend including a classic against Kyrgios, said it had been a dream to win the title on home soil.
"For us, so many emotions. It's been an unbelievable rollercoaster," he said, "Bjorn, you're a great captain, and Rocket (Rod Laver), thanks for being here today.
"It makes it more special. It's been a dream weekend for me to be playing in Switzerland. Thank you for all the noise you've made, I've loved every moment," he added before joining his team to be presented with the trophy by Australian great Laver as blue ticker-tape rained down on the court.
The event, sanctioned by the men's ATP tour for the first time this year, will be staged in Boston in 2020.