
Second-seeded Federer, who won the last of his five US Open titles back in 2008, took on 55th-ranked Australian John Millman under the lights on Arthur Ashe Stadium while Djokovic, victor in NY in 2011 and 2015, tackled Joao Sousa.
Federer started in typical fashion to take the opener 6-3 but Millman didn't wilt, taking the game up to the Swiss to win the next two 7-5, 7-6.
It would be their earliest meeting in a Grand Slam since 2007, when Federer defeated Djokovic to reach the Australian Open quarters.
Before their match, Roger Federer said he had a great deal of respect for his Australian counterpart.
Roger Federer beats Yoshihito Nishioka at US Open to reach second round
She faces Cîrstea, who was nearly beaten by American Alison Riske, before making a comeback to beat Riske 7-5 in the decider. The 37-year-old hit 56 winners as he put on another show in Arthur Ashe Stadium , easing to a 6-2 6-2 6-4 victory.
Federer had struggled with his timing in the early stages of his previous match against Nick Kyrgios before clicking into gear, but against Millman he just could not find his game.
Federer broke Millman's first service game, led 3-0 and took the first set in just 33 minutes, finishing it off with a 128 miles per hour serve and backhand volley victor.
Following an injury interrupted campaign in 2017, Millman closed out the calendar year ranked 128th overall.
A Federer v Djokovic clash would provide the flawless contest to propel the US Open into the second week, with the two champions having claimed seven titles at Flushing Meadows between them.
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The 20-time Grand Slam champion double-faulted 10 times, including twice in a row during the final tiebreaker. "Definitely a player I've looked up to throughout my career", he said before the match.
Kei Nishikori, runner-up in 2014, was also pleased to get through in three sets in blazing sunshine on Louis Armstrong Stadium. "But I have never been a fan of playing someone's reputation". He was up a break in the second set, before his serve began to betray him.
Roger Federer believes that the points distribution in Grand Slams is not really the best possible one. Federer broke him to go up 4-2 in the fourth set, but Millman broke right back, leading to the tiebreak.
Keys has been solid in NY, having dropped a single set through four matches, and turned it up a notch against her 29th-seeded opponent as she lost only 10 points on serve during a 76-minute match in which she was broken once.
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