John Millman pulled off one of the greatest upsets in US Open history as he dumped Roger Federer out in a dramatic four setter on Monday night in NY.
Japan's Kei Nishikori also reached the last eight, beating Philipp Kohlschreiber 6-3, 6-2, 7-5.
With the US Open's heat advisory put back into effect, the pair traded punishing groundstrokes under the blazing sun and it was Cibulkova who was often pinned well behind the baseline and at the mercy of her opponent.
Federer started well, racing through the first set and unsettling Millman by dropping the ball short.
His match didn't get to the point of a heat interruption, because he wrapped it up in straight sets, but that did come into play for a couple of women's matches. But he somehow clawed his way back to win 3-6 7-5 7-6 (8/6) 7-6 (7/3).
Federer, like any great champion, refused to throw in the towel and showed emotion for the first time after breaking for a 4-2 lead in the fourth.
"I don't think she was struggling so much", Vondrousova said.
The Australian is ranked No 55 in the world and for his heroics will be rewarded by a quarters clash against Novak Djokovic.
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The upset for the ages looked remote when Federer broke Millman - playing his his first fourth-round match at a slam at age 29 - in the second game of the match en route to taking the opening set in routine fashion. 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.
The defending US Open champion would not be denied and fired his seventh ace on match point to end the three hour, 20-minute tussle 6-3 6-3 6-7 (6-8) 6-4.
An elbow injury forced the 31-year-old out of the 2017 tournament though Djokovic reached the final 12 months previously, beaten by Stan Wawrinka.
What at first seemed like a routine victory became anything but.
In the women's draw, Maria Sharapova was delivered a surprising upset at the hands of Spain's Carla Suárez Navarro.
Cilic, who beat Nishikori four years ago for his only major title, was a 7-6 (6), 6-2, 6-4 victor against No. 10 David Goffin, while Nishikori advanced by defeating Philipp Kohlschreiber 6-3, 6-2, 7-5.
"I felt like a bit of a deer in headlights to begin with, to be honest with you", Millman said.
However, the 37-year-old Swiss delivered a strangely lethargic performance on Arthur Ashe Stadium - prompting some pundits to question whether he was 100 per cent fit - and Millman capitalised superbly to earn the biggest win of his career by far.