Schwartzman, the 29th seed at Flushing Meadows, turned on the style to beat Janko Tipsarevic 6-2, 6-4, 7-5 and set up a meeting against fifth seed Marin Cilic.
Dudi Sela's run at the US Open is over after he was eliminated in straight sets by 17th seed Sam Querrey of the USA.
A first-round winner over wild card Christopher Eubanks, succumbed 6-4, 6-1, 6-4 in a match lasting one hour, 20 minutes.
Querrey, standing at 6ft 6" sent down 19 aces to Sela's one. He also had a conversion rate of 71 per cent on break points, and hit 35 winners to Sela's 12.
