The packed crowd erupted as Van den Bergh achieved perfection in the sixth set, levelling the thrilling contest and ultimately forcing a dramatic decider.
Despite Van den Bergh breaking throw in the final set, van Gerwen looked set to respond, but a surprising error and a missed dart at the bullseye opened the door for Van den Bergh, who coolly took out 16 for the biggest win of his career.
Van den Bergh now faces a tough quarter-final against Nathan Aspinall, who battled his way to a 4-1 win over Cameron Menzies despite not being at his best.
Elsewhere, teenage sensation Luke Littler continued his meteoric rise with a dominant 4-0 demolition of James Wade, averaging an impressive 105.47.
Littler will face Jonny Clayton in a highly anticipated televised clash, after Clayton survived a scare, recovering from behind to edge out Ryan Searle 4-3.
World number one Luke Humphries maintained his impressive form with a straight-sets victory over Josh Rock.
Humphries, who survived a set dart early on, will meet Damon Heta in the quarter-finals. Heta himself was involved in a nail-biting encounter, overcoming a match dart against Gerwyn Price after the Welshman had fought back from 3-1 down to level.
Defending champion Stephen Bunting kept his hopes of retaining the title alive with a hard-fought 4-2 win over veteran Peter Wright.
Bunting will face Danny Noppert in the last eight, following Noppert’s comfortable 4-0 victory over William O’Connor.
The quarter-finals take place on Sunday afternoon, with the semifinals and final scheduled for the evening session. Darts fans are in for a treat as the tournament reaches its climax.