The 21-year-old trailed 5-1 before reeling off five consecutive legs to complete an unlikely turnaround and set up a second-round meeting with Mike De Decker.
“I don’t know what just happened,” Schmidt said after the match.
“The first half of the match wasn’t the best, but then things just clicked and went my way.
“I really came here believing that I’m capable of winning on the European Tour, and I took this belief on to the stage.”
Elsewhere, Niko Springer delighted the home crowd with a resounding 6-2 victory over Darius Labanauskas, averaging 105.21 to book a meeting with top seed Gian van Veen.
Max Hopp also enjoyed a notable win, knocking out former world champion Rob Cross 6-3 to continue the German success in Leverkusen.
Kevin Doets recovered to beat Dominik Gruellich and will face Jonny Clayton in the second round, while Joe Cullen overcame Charlie Manby to earn a meeting with five-time champion Michael van Gerwen.
Rob Owen survived a deciding leg to defeat Andrew Gilding after hitting eight 180s, setting up a clash with Damon Heta. Karel Sedlacek and Sebastian Bialecki also came through last-leg deciders, as Maik Kuivenhoven compounded Daryl Gurney's disappointing week.
Mickey Mansell, Kim Huybrechts, Dirk van Duijvenbode, Niels Zonneveld, Ryan Joyce and Bradley Brooks were also among the first-round winners, while Dragutin Horvat secured his first European Tour victory since 2023 by beating Mario Vandenbogaerde.
Results
Round one - afternoon
Ryan Joyce 6-1 Mio Varila
Karel Sedlacek 6-5 Rhys Griffin
Dragutin Horvat 6-2 Mario Vandenbogaerde
Rob Owen 6-5 Andrew Gilding
Jan Schmidt 6-5 Cameron Menzies
Mickey Mansell 6-1 Michal Smejda
Bradley Brooks 6-2 Lukas Wenig
Dirk van Duijvenbode 6-3 Jaimy Van de Weerd
Round one - evening
Kim Huybrechts 6-1 Samuel Price
Maik Kuivenhoven 6-3 Daryl Gurney
Sebastian Bialecki 6-5 William O'Connor
Max Hopp 6-3 Rob Cross
Joe Cullen 6-4 Charlie Manby
Kevin Doets 6-4 Dominik Gruellich
Niko Springer 6-2 Darius Labanauskas
Niels Zonneveld 6-2 Daniel Klose