Federer got his great rival's input at his shoulder before rallying late and raising his game in the decisive super-tiebreaker to beat Nick Kyrgios 6-7 (5), 7-5, 10-7 in the afternoon session.
"What I really enjoy with Rafa is just that we very often align, our ideas align," said Federer, praising Nadal for "clarity in his advice."
With the European team's captain, Bjorn Borg, also in the huddle, it brought a total of 50 Grand Slam singles titles together to help Federer edge past Kyrgios. The Australian had world team captain John McEnroe's seven Grand Slam titles in his chair.
Nadal got the favor back from Federer during a 6-3, 7-6 (1) win over Milos Raonic that opened the evening session. He was quickly back on court, partnering Stefanos Tsitsipas in the day's doubles rubber.
Kyrgios and Jack Sock won that match 6-4, 3-6, 10-6, scoring two key points for the world team, which trails Europe 7-5 ahead of the final four matches Sunday.
The third edition of the annual Laver Cup is decided Sunday by a doubles match, then three more singles -- each worth three points with 13 needed for overall victory.
Federer, who co-owns the Laver Cup competition, delighted a 17,000 crowd in his first singles match in his native Switzerland this season. He partnered Zverev to a doubles win on Friday.
"Today was extremely loud. I don't recall that on the tour ever being almost this loud," the 38-year-old Federer said of the Palexpo indoor arena in Geneva. "You know, if I would have retired a long time ago, I wouldn't have this moment right now."
Federer broke the Kyrgios service at 5-5 in the second set and then produced some of his best tennis in the decisive tiebreaker.
"I think the guy I was playing was just pretty good. Don't you think so?" said Kyrgios, when asked at a postmatch news conference if his own play lacked something in key moments.