It was a match of contrasting fortunes for the players, with second seed Gaultier taking the first and the Englishman taking control in the second - then emphatically in the third - before the Frenchman fought to regain supremacy and eventually clinch an 8-11, 11-8, 2-11, 11-6, 11-4 victory after a 82-minute marathon encounter.
Gaultier will now face Ramy Ashour, the defending champion from Egypt. The No3 seed recovered from losing the third game in an earlier quarter-final to beat England's No7 seed Peter Barker 11-8, 11-3, 9-11, 11-8 in 51 minutes.
For most of the match, the gifted young Egyptian was in a world of his own as he pulled off spectacular shots which entranced the partisan crowd which was willing the Cairo man to win.
Meanwhile, tall Englishman James Willstrop continued his giant-killing run in Kuwait by beating eighth-seeded Frenchman Thierry Lincou in the opening quarter-final match of the night.
It was only 24 hours earlier that Willstrop made his first appearance on the Green Island court - where the 11th seed pulled off the event's biggest upset when he despatched favourite Karim Darwish.
The 26-year-old was in dominant form throughout tonight's match against the 2004 champion, winning 11-9, 11-5, 11-5 in 49 minutes.
In the next round, Willstrop will meet Amr Shabana, the Egyptian who is adored by the Kuwait crowd.
Much to the delight of the packed crowd, Amr Shabana beat fellow Egyptian Wael El Hindi in straight games to reach the World Open semi finals for the fifth time in a row.
Fourth seed Shabana, three-times a winner of the title, romped to a first game win - but El Hindi, the ninth seed, came back with more opposition in the next two games.
But it was the left-hander Shabana who ultimately maintained the upper hand, wrapping up his 11-1, 11-5, 11-9 win in 40 minutes.