Nishikori, a 2014 finalist at the US Open, lost to 38th-ranked Alex De Minaur 6-2, 6-4, 2-6, 6-3 in the third round, leaving less than half of the top 12 men still in action. De Minaur, a 20-year-old Australian who has won two tour events this year, including last month's hard-court tuneup in Atlanta, outlasted Nishikori from the baseline and took advantage of his opponent's 60 unforced errors.
"This is where I feel like my game's at,'' De Minaur said. "I want to be pushing these guys, I want to be pushing second weeks of Grand Slams and putting myself out there.''
Federer, who struggled early in his two previous matches, had no such trouble Friday and won in straight sets for the first time in this year's tournament, downing Daniel Evans 6-2, 6-2, 6-1 to advance to the round of 16.
"At the end of the day, I think what matters the most for me is that I am in the [fourth] round, after all, after those two sort of slow starts," Federer said. "Give myself another opportunity to do better, and I did."
The No. 3 seed and five-time champion at Flushing Meadows will make his 18th appearance in the round of 16 at the US Open, breaking a tie with Jimmy Connors for the most among men in the Open era. Federer, 38, is also the oldest man to reach the fourth round since a 39-year-old Connors made it into the semifinals as a wild card in 1991.
On Friday, Federer hit 48 winners to Evans' seven and had a 10-0 advantage in aces while winning the match in just 1 hour, 20 minutes.
Federer had dropped the opening set in his first two matches for the first time in his 19 US Open appearances. No man has done that and gone on to win the tournament, but the No. 3 seed isn't one to worry about history.
Nor is he superstitious, which is why he didn't care when asked if it was OK if his family and support staff moved from their usual spot in the stadium to another, where they could find more shade. Supporters of Evans were on the sunny side.
"Brits maybe need a little bit of sun sometimes," Federer joked in his on-court interview.
In the last match in Ashe at the end of the night, defending champion and No. 1 seed Djokovic's left shoulder looked just fine in a 6-3, 6-4, 6-2 victory over Denis Kudla of the United States.
During his win Wednesday, Djokovic was visited several times by a trainer for treatment on the shoulder, which he said was hurting quite a bit. But that did not appear to be an issue at all against Kudla.
"I managed to play almost pain-free," Djokovic said. "That's a big improvement."
Also on Friday, Dominik Koepfer beat No. 17 Nikoloz Basilashvili 6-3, 7-6 (5), 4-6, 6-1 to advance to the round of 16, becoming only the second qualifier to make it that far in this tournament in the past decade.
Koepfer, a 25-year-old German ranked No. 118, has made the most of his first appearance at Flushing Meadows, downing established tour players Ryan Harrison and Nicolas Mahut in qualifying rounds and Reilly Opelka in the main draw. By beating Basilashvili, Koepfer joins Denis Shapovalov in 2017 as the only qualifiers to reach the Open's fourth round since 2009.
Through three rounds of qualifying and three rounds in the main draw, Koepfer already has been on court just shy of 13 hours. But he said after his match Friday that it doesn't matter. "I like winning, so I'm going to keep going.''
The Associated Press contributed to this report.