The world championship debutant, who had beaten compatriot Martin Schindler in round one, forced a deciding leg in the opening set and a third 180 then helped secure an 11-dart finish.
Van Den Bergh - forced to miss last month's Grand Slam of Darts after contracting COVID-19 - regrouped and swiftly reeled off three straight legs to level with a nerveless 142 checkout.
After losing the opening leg, Hempel stopped the rot to turn around the third set and continued his momentum into the fourth - taking it 3-0 with a cool 64 finish to pull off the biggest upset of the tournament so far.
"I met one of the best players in the world, but tonight it was my game and I felt comfortable," Hempel, who has only been playing for four years, said on Sky Sports.
"It has been amazing to get here and now I am in the third round. This tournament is the biggest in the world, but I felt comfortable on the stage and I love it here."
There was no such drama for former world championship runner-up Michael Smith, who landed six maximums as he coasted to an impressive 3-0 win over Ron Meulenkamp.
Dutch left-hander Meulenkamp had beaten Lisa Ashton in the opening round, but was swept aside following a blistering display by the ninth seed.
'Bully Boy' Smith - beaten by Michael Van Gerwen in the 2019 final - gave up only one leg in the match, during which he averaged just over 106 and returned a 75 per cent checkout rate.
Tuesday's late match saw Australian qualifier Raymond Smith end the hopes of South Africa's Devon Petersen, beating the 28th seed 3-0 to set up a third-round match against Hempel.
Vincent Van Der Voort earlier produced a 3-0 victory over Adam Hunt, who had hit five maximums and boasted the higher match average at 92.01. The Dutchman will next meet fourth seed James Wade for a place in the last 16.
In Tuesday's afternoon session at Alexandra Palace, Mervyn King battled through to the third round with a 3-2 comeback win over Ryan Joyce, reeling off nine consecutive legs and a 110 checkout on match darts.
World number 14 Dave Chisnall, a semi-finalist last year, saw off Belgian Mike De Decker 3-0, firing in back-to-back 12-dart legs.
Welsh 19-year-old Lewy Williams marked his world championship debut with a 3-0 win over Toyokazu Shibata in their first-round match.
Jason Lowe also did not drop a set as he coasted through against Daniel Larsson and will go on to play seventh seed Jose De Sousa.