De Minaur scraps past local legend van de Zandschulp
The top-seeded 26-year-old displayed his fighting qualities to see off a spirited challenge from the world number 65, who had never made the quarter-finals of his "home" tournament.
"Yeah, a battle. It was nothing short of that. It was topsy-turvy but a huge mental effort from my part," said de Minaur after his 3-6, 7-6 (7/4), 7-5 victory.
"This match was all about trying to dig in, find a way and if you hang in long enough, you can get there," he said.
Van de Zandschulp had never beaten the world number eight, but delighted the Rotterdam crowd by taking the first set 6-3, helped by winning nearly 90 percent of his first-service points.
The Dutchman had a chance to take a stranglehold on the match in the crucial seventh game of the second set, but squandered a break point with an ill-judged drop shot, allowing de Minaur to hold serve.
The set eventually went to a tie-break, which De Minaur took 7-4, helped by a Van de Zandschulp double fault and some solid serving of his own.
To groans around the Rotterdam Ahoy Arena, van de Zandschulp dumped a backhand into the net to concede the second set and set up a decider.
The pair traded breaks early in the third but neither was able to seize the initiative until 5-5 when De Minaur capitalised on a simple backhand volley error by the Dutchman to break serve.
That gave him the chance to close out the set 7-5 and the match, as his valiant opponent hit a tired-looking backhand into the bottom of the net.
'Find my range'
"I would love to hit the ball a little bit cleaner and find my range," said De Minaur, who admitted he was "too negative" with himself throughout the match.
De Minaur is hoping to make it third time lucky in Rotterdam after losing in the final the last two years to the world's top two, Carlos Alcaraz and Jannik Sinner.
His chances this year have been boosted by the fact neither is playing. Alcaraz withdrew on the eve of the tournament after his epic efforts to win the Australian Open.
Awaiting De Minaur in the semis is Frenchman Ugo Humbert who despatched Australian qualifier Christopher O'Connell with relative ease 6-4, 6-1.
On the other half of the draw, second seeded Felix Auger-Aliassime from Canada also faces local talent in Tallon Griekspoor.
In the other quarter-final third-seeded Alexander Bublik of Kazakhstan takes on Jaume Munar from Spain.