Schwartzman, the 20th seed, matched his run from the 2017 tournament and could next face three-time Flushing Meadows champion Rafael Nadal, who takes on 2014 winner Marin Cilic in a later fourth-round clash.
- Berrettini joins select club -
Matteo Berrettini became just the second Italian man to progress to the US Open quarter-finals, 42 years after Corrado Barazzutti's run to the last four in New York.
Berrettini, the 24th seed, eased to a 6-1, 6-4, 7-6 (8/6) win over Russia's 43rd-ranked Andrey Rublev to reach the last eight at a Grand Slam for the first time.
"It's something really crazy. I cannot believe it right now. I need a few hours to understand what happened," said Berrettini, 23, who goes on to play French 13th seed Gael Monfils or Spaniard Pablo Andujar.
"I'm just happy. Seeing my team and family here and crying, for me it's unbelievable."
Berrettini went one step further than his run to the last 16 at Wimbledon in July, where he was beaten by Roger Federer.
The Italian overcame a momentary lapse against Rublev as he dropped serve at 6-5 in the third set but sealed victory after two hours and 11 minutes in a tense tie-break.
"I think I did an unbelievable match. I thought Andrey was playing really good and playing with confidence," Berrettini said.
"I was mixing my tennis, using the slice, forehand and serve. I think all my weapons were really good today."
Andujar, 33, will try to become the oldest player in the Open era to reach his first Grand Slam singles quarter-final as he battles Monfils, a semi-finalist at Flushing Meadows three years ago.