Maguire’s assured success over the four-time world champion set up a last-eight clash with David Gilbert, who beat Ryan Day 4-3 in round four despite Day’s third-frame 129.
Another former world champion, Mark Williams, had no such problems as he beat Sam Baird 4-2. Next up for the Welshman is Stuart Bingham after his 4-0 whitewash of Martin O’Donnell.
Mark Selby also shut out his last-16 adversary, Jimmy Robertson, and he goes on to plays Martin Gould, conqueror of Anthony McGill.
Gould is in strong form, knocking in breaks of 137 and 107 against the Scot – though Selby looked equally impressive in his one-sided victory over Robertson, finishing off with a rousing 132 clearance.
The fourth quarter-final pits Mark Davis against Gary Wilson, with the tournament being played to a conclusion on Sunday at the Topsport Centrum.
The European Tour event is the first professional snooker tournament in The Netherlands for over 20 years.
Round four results
Mark Selby 4-0 Jimmy Robertson
Martin Gould 6-1 Anthony McGill
Mark Williams 4-2 Sam Baird
Stuart Bingham 4-0 Martin O’Donnell
Stephen Maguire 4-1 John Higgins
Gary Wilson 4-2 Joe Swail
David Gilbert 4-3 Ryan Day
Mark Davis 4-1 David Grace