The victor of that match will meet Schwartzman, a 25-year-old Argentine, in the fourth round of a major for the first time, or 16th-seeded Lucas Pouille of France.
He converted nine of 20 break points and was aided by a whopping 80 unforced errors from the 2014 champion, who entered the tournament short on match play after having skipped Montreal and Cincinnati due to injury.
Williams faces Greece's Maria Sakkari and is hoping to make the competition's fourth round for the third year in succession; a home crowd is sure to have its advantages for the 37-year-old.
Schwartzman played far from a ideal match, committing 48 unforced errors and almost squandering a double-break lead in the fourth set, but he hung on to win in three hours and 23 minutes. I think in every match I can win.
The 2006 champion remains undefeated in night matches played on Arthur Ashe Stadium, and it might take more than just Serena Williams (next year at the earliest) for that streak to come to an end sometime soon. I'm more than blessed... "Is not just for the tall guys". When he takes on Shapovalov in the fourth round, he will create history as it will be the first time in the Open Era that a player faces four qualifiers at a Grand Slam. "I am playing well and try to be like this every match".
"I guess it's like an upper thoracic back problem", Edmund said". And no qualifier had reached the last 16 since Gilles Muller in 2008.
"The month of August has been absolutely life changing for me", says the Canadian. "But I was always like this and I always try to improve my tennis and try not to think about other things".
Wimbledon semi-finalist Sam Querrey advanced to the last 16 at his hometown Grand Slam tournament for the first time since 2010 after defeating Radu Albot in four sets, but countryman John Isner was not so lucky, knocked out in straight sets by German veteran Mischa Zverev.
Asked about how open the bottom half of the men's draw has become with the Cilic upset, the American said: "Everyone was watching that in the locker room". He's obviously really good.
In what has been his breakthrough year, the little Argentinian came into the tournament in fine form. "Even before that I think guys saw that it was open". Whoever emerges from Cilic's quarter and Zverev's quarter will be players who typically don't reach the second week, much less the semifinals.
The 1.7-meter (5-foot-7) Argentine did his best on Friday to prove size doesn't matter against the 1.98-meter Croatian and managed to do so for one day at least on the hard courts at Flushing Meadows, Efe news reported. He was also in the quarterfinals at the Australian Open. Then there are the young players who might one day be major contenders, but who are breaking through earlier than expected. I really just couldn't pass him is what it comes down to, plain and simple. I don't know what it is.