Switzerland's Federer may well have decided the match when serving at 3-all, love-40, less than 20 minutes into his game against controversial Australian Kyrgios on Sunday morning (NZT).
Things went from bad to worse for a younger player, losing his serve again in the second game of the second set following a forehand victor from Roger, who had won six games in a row.
At night, 13-time major champion Novak Djokovic easily beat No. 26 Richard Gasquet 6-2, 6-3, 6-3 in Ashe, while 2014 U.S. Open title victor Marin Cilic met 19-year-old Alex de Minaur in Armstrong in the day's last match.
EPTEMBER 01: Dominika Cibulkova of Slovakia shakes hands with Angelique Kerber of Germany after their women´s singles third round match on Day Six of the 2018 US Open at the USTA Billie Jean King National Tennis Center on September 1, 2018.
"I think to play fair and play tough", he said. "I definitely think it was a special one, no doubt about it", he told reporters after his victory.
The first set was the only competitive one, when Kyrgios's best qualities were on display and Federer hadn't quite settled in yet.
Federer was 21 when he won his first Slam at Wimbledon in 2003 and admitted he's happy to be regarded as a role model, if not necessarily for Kyrgios.
The Australian had already found himself at the centre of a Flushing Meadows controversy this week when umpire Mohamed Lahyani felt it necessary to get down from his chair during Kyrgios's second round match against Frenchman Pierre-Hugues Herbert to urge him to show some interest.
Two seeded men lost in the afternoon to unseeded opponents: No. 4 Alexander Zverev and No. 17 Lucas Pouille.
Kohlschreiber will seek a quarter-final berth against 2014 runner-up Kei Nishikori after the Japanese downed Argentine Diego Schwartzman 6-4, 6-4, 5-7, 6-1.
"Look, I know that I'm the clear favorite in the match", Djokovic said.
True to form, Kyrgios had already been responsible for some drama in NY this week after being forced to defend himself against claims that an umpire had improperly helped coach him to victory during his second-round match against Pierre-Hugues Herbert. On the first three, Kyrgios missed a shot.
When she ripped a backhand victor to claim the third set's opening game on Sunday, Williams let out her loudest shout of the day, leaning forward and rocking both arms. She then faced a break point, but Kanepi wasted that chance by sending a backhand wide. "But it's Roger", smiled Kyrgios. "He loosened up straightaway after that".
"But I think, you know, just the way he goes about things, I could take a leaf out of his book".
He had break points in eight different games, putting Andy under a lot of pressure, and he broke him seven times from 10 opportunities to keep the scoreboard on his side all the time. "When he gets in front, there's not much you can do".