Federer, 37, rushed to Zverev’s side during a nail-biting second set in the penultimate Laver Cup match.
Europe needed to win to avoid it going to a decider and Federer was anxious to tell Zverev to change his tactics.
The 20-time Grand Slam champion urged Zverev to move forward and not back to avoid Anderson dominating the rallies.
Zverev barely flinched as Federer deliver a courtside monologue but it proved to be key as the 21-year-old fought back to take the set and the match.
Victory ensured Team Europe retained the trophy – 12 months after winning the first ever edition of the tournament.
Team Europe players stormed on to court at the end before Zverev hit out at Federer’s coaching ability.
“Roger is not a good coach,” he laughed – before admitting: “He helped me a lot. He gave me some tactical advice and it worked.
“I won the second set and I won the match tie-break. It was a team effort, everyone supporting, the energy was unbelievable.
“It was a pleasure to play here and I hope one day the Laver Cup will come back to Chicago.
“It was an unbelievable weekend. We all love it, we enjoy it so much we want to play it every weekend but unfortunately we have other tournaments to play in.”
Federer and Zverev had earlier combined in the doubles but Sock and Isner were too strong.
That kept alive Team World’s hopes of an unlikely comeback win but in the end it was too steep an ask.
“I felt like everything we did in the doubles was my mistake. Roger does a double fault and it’s my fault!” Zverev joked.
“I tried to keep up with him but it was a great experience. We lost the match tie-break but we made up for it in the end.”
Beaten captain John McEnroe paid tribute to the opposition and said: “First of all I’d like to congratulate Team Europe.
“It was a great match, a great effort, unbelievably exciting.”
It was announced at the presentation ceremony that next year’s event would be back in Europe at Geneva.
Geneva’s mayor Sami Kanaan said: “As the mayor of Geneva, I’m extremely happy to announce that Geneva will be the host city of the next Laver Cup in September 2019.
“We are already preparing ourselves actively to welcome this exceptional event and to become the capital of tennis around the world.”
What did Roger Federer say to Alexander Zverev in crucial coaching chat?
“You can return from where Bjorn [Borg, Team Europe’s captain] said or you can find your return position.
“But once the rally gets going, you have to remind yourself to keep your position or move forward. Stop moving back and back and back.
“That’s why he’s able to get all these volleys because he has too much time, he gets a metre or two closer to the net.
“He gets a split second more time to get his legs in position or to run around, all this stuff.
“If you get closer to the baseline he won’t have that time. That’s my opinion.
“You slice and you come back so just stay in that position. Then you can also see the short balls.
“Back there you don’t have any short balls anymore so it’s hard to stay offensive.”