A recent US Open quarter-finalist, world No.69 van de Zandschlup claimed the first top-10 win of his career.
The 26-year-old also advanced to the semi-finals of an ATP event for the first time.
There, he will face 2011 champion Marin Cilic, who was a 6-4 3-6 6-3 winner over No.3 seed Roberto Bautista Agut.
Denis Shapovalov was another big-name casualty in Russia, the No.2 seed going down 4-6 3-6 against world No.53 Jan-Lennard Struff.
Although, there were better fortunes for No.5 seed Taylor Fritz. The Indian Wells semi-finalist is yet to drop a set this week after prevailing 6-4 6-2 against Australia's John Millman.
Elsewhere, Matteo Berrettini was the victim of another upset at the Erste Bank Open in Vienna.
The Wimbledon champion went down 1-6 7-6 (7-2) 6-7 (5-7) after a two-hour 40-minute battle with Carlos Alcaraz.
Reaching his first ATP 500 semi-final, the Spanish teenager claimed another big scalp having defeated Stefanos Tsitsipas at Flushing Meadows last month.
However, No.2 seed Alexander Zverev remained on course for a fifth title of the season, as he claimed his 300th tour-level win.
The Australian Open finalist beat Felix Auger-Aliassime 6-4 3-6 6-3, avenging his fourth-round defeat by the Canadian at Wimbledon in July.