Sock and Kyrgios won Saturday's doubles 6-4, 3-6, 10-6 after Nadal defeated Milos Raonic in his first match since his US Open triumph in the singles.
"There was a lot on the line there," said Sock. "We obviously wanted to keep the overall weekend close. Being down 9-3 is different than 7-5.
"We've had so many chances this weekend, it's been crazy, so I think the score could be the other way round.
"I thought it was a high quality match and we're definitely happy to get the win."
Nadal, who won his 19th Grand Slam title in New York, had earlier overcome Canada's Raonic 6-3, 7-6 (7/1) after defending eight break points in the first set.
"I feel very lucky," said Nadal. "I think he deserved that first set for sure. Later in the match I think I started to play a little bit better."
"The crowd could feel it, I could feel it. I needed to get some energy going but you can't do that if you don't play any good shots and Nick was playing very well," said Federer, the 20-time Grand Slam champion.
"I was just trying to stay focused. If you can turn the momentum, the crowd gets back into it and I need some earplugs next time, it was just phenomenal."
Bjorn Borg's holders had seen Team World draw level with John Isner's victory over Zverev.
Isner fought back from a set down to beat Zverev 6-7 (2/7), 6-4, 10-1 and haul Team World level at 3-3 after Europe led by two points after the opening day.
The scoring system sees one point awarded for each win on the first day, two points given for each victory on the second day, and three points on offer in each match on Sunday's final day.
This year is the first time the tournament has been played since being added to the ATP Tour.
Europe won the 2018 edition 13-8 in Chicago.