But he was undone as Argentine Schwartzman, seeded 29th, came from a set down to claim a 4-6 7-5 7-5 6-4 success over the Croatian fifth seed.
The win, Schwartzman's second win over a Top 10 player, moved him into the second week of a major tournament for the first time.
"I didn't have luck with the draw", Schwartzman said of his lack of success in majors.
The upsets that have unfolded in the bottom half of the draw will result in there being at least two first-time US Open quarter-finalists; of the remaining men in this part of the draw, only Kevin Anderson (2015) and Lucas Pouille (last year) have got this far at Flushing Meadows.
The tournament is without the injured Andy Murray and Stan Wawrinka as well as Novak Djokovic, who has ended his season.
"Kind of a freak year with all these injuries", said Querrey, 29, who has never made it past the fourth round of the Open.
"Every grand slam, it's a chance for young guys to prove themselves and I have been doing that". A quarterfinalist in 2011, Isner is always looked at as a danger in any tournament he plays thanks to his fearsome serve. He has a hard match with Schwartzman in the third round with the Argentinian in good form. "Hopefully it's nothing too serious", said Shapovalov.
Shapovalov next faces 12th seed Pablo Carreno Busta, who finds himself in the unprecedented position of taking on four successive qualifiers.
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). The Tennis Channel will be running a preview show between 8 a.m. -11 a.m. ET, along with replays through the days and nights of the tournament.
The teenager is the youngest man to reach the fourth round of a grand slam in almost 20 years and looks to be heading quickly for the top of the game.
"Obviously I'm super-excited", USA ninth seed Venus said.
Awaiting Muguruza next is Czech 13th seed Petra Kvitova, who defeated French 18th seed Caroline Garcia 6-0, 6-4. "Words can't describe it".
The 37-year-old proceeded to reach the last 16 of a major for the seventh consecutive time, defeating Greece's Maria Sakkari in straight sets to line up a fourth round meeting against Spain's Carla Suarez Navarro.
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. For players like Isner and Querrey, it's the opportunity of a lifetime-a plausible road to the final of the U.S. Open, with no obvious insurmountable challenge in their way.
She eliminated Venus Williams and already ousted second-ranked Simona Halep from the top spot chase.
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. Only current number one Karolina Pliskova and fourth-seeded Elina Svitolina could deny her reaching the top for the first time.