The victor will play Novak Djokovic, who easily accounted Joao Sousa of Portugal 6-3, 6-4, 6-3 earlier in the day.
The Spaniard will be at that stage for the second time at the US Open, five years after her other run to that round.
He improved to 28-0 at the U.S. Open against opponents ranked outside the top 50, and here's another reason it wasn't all that surprising the way things went against Sousa: Djokovic is now 5-0 in their head-to-head series, taking all 14 sets they've played against each other.
Federer, indeed, did not play as well as he had in the opening three matches, when he didn't drop a set.
"It's a dubious call to me because he's let it happen so many times", commentators were heard saying about a late Sousa challenge call by the umpire. "But you know I have so much respect for Roger and everything he's done for the game".
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The two-time champion, who is now 28-0 in NY against players outside the Top 50 of the ATP Rankings, is bidding to lift his third US Open title on his first visit to the tournament since reaching the 2016 final.
The Australian is ranked No 55 in the world and for his heroics will be rewarded by a quarters clash against Novak Djokovic.
The heat, though, is much tougher on Djokovic, who showed the same blank expression, rosy cheeks and sweat-soaked shirt as during his first-round match last week. In fact, he has never won an ATP event, falling in the final to Marco Cecchinato of the Hungarian Open earlier in April, according to a report on the website of US Open.
Nishikori missed the U.S. Open previous year because of a right wrist injury. Suarez Navarro let the 22nd-seeded Sharapova create her own problems.
"I felt like a bit of a deer in headlights to begin with, to be honest with you", Millman said.
Coming into the match the number-two seed, Federer saw set point slip away from him twice, in the second and third sets, as the resilient Australian, Millman, playing his first-ever Grand Slam fourth-round match, held his nerve.
The 19-year-old Vondrousova, who said she dealt with cramping, certainly helped decide the outcome: Of Tsurenko's 107 points, only 17 came via winners; 73 were her opponent's unforced errors.