Among the eight players left - Schwartzman, Zverev, Carreno Busta, Sam Querrey, Paolo Lorenzi, Kevin Anderson, Denis Shapovalov and Lucas Pouille - only Querrey has reached the semi-final of a Grand Slam once (Wimbledon 2017), and they only have five Grand Slam quarter-finals appearances between them.
Schwartzman, ranked No. 33 in the world, will next face 16th seed Lucas Pouille, a 2-6, 6-3, 6-4, 6-4 victor over Russia's Mikhail Kukushkin.
"I didn't do many mistakes", Schwartzman said after taking out Cilic.
Last year, Schwartzman lost in the first round of all four majors. Many (top) players are injured this week.
"Kind of a freak year with all these injuries", said Querrey, 29, who has never made it past the fourth round of the Open. "I am playing well and try to be like this every match". I struggle playing at night at this tournament.
"In the final game of the match, I think I started to be a little bit nervous", Schwartzman admitted afterwards. "Hopefully it's nothing too serious", said Shapovalov.
American Isner has also been knocked out of the tournament, losing 6-4 6-3 7-6 to Germany's Mischa Zverev, who is enjoying his best ever run at Flushing Meadows, having previously failed to get past round two.
Marin Cilic, of Croatia, returns a shot from Diego Schwartzman, of Argentina, during the third round of the U.S. Open tennis tournament, Friday, Sept. 1, 2017, in NY.
The Spaniard, who has not dropped a set, will become the first player to face four qualifiers at a Grand Slam in the Open Era (since 1967).
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The draw certainly looks more inviting to Zverev than when he reached the fourth round at the Australian Open this year.
Awaiting Muguruza next is Czech 13th seed Petra Kvitova, who defeated French 18th seed Caroline Garcia 6-0, 6-4.
The elder of the Williams sisters was delighted to hear of the news, saying: "Obviously, I'm super-excited".
The 13th-seeded Kvitova is in the fourth round at Flushing Meadows for the third time in a row. "Words can't describe it".
The 2017 U.S. Open spotlight returns to the lower half of the bracket on Friday as competitors attempt to book a place in the fourth round.
Surprise exits have been something of a theme at this year's U.S. Open thus far, and the opportunity is there for Muguruza to add the American major to her trophy cabinet after a series of high-profile departures in the women's competition.
Sharapova, the 2006 US Open victor, has already beaten Halep and Hungary's Timea Babos in her first Grand Slam since serving a 15-month doping ban after testing positive for the blood booster meldonium, at the 2016 Australian Open.
Two of the others, current No. 1 Karolina Pliskova and Elina Svitolina, will play Saturday.
She eliminated Venus Williams and already ousted second-ranked Simona Halep from the top spot chase.
"It means a lot", she said.