Van Veen looked set for an early exit after falling 5-2 behind against Dimitri Van den Bergh, who was competing in his first European Tour event for more than a year.
The 24-year-old Dutchman, however, won four successive legs to seal a dramatic 6-5 comeback victory and book a meeting with Dave Chisnall.
“Dimitri, scoring-wise, today wasn’t really up to par, but he finished really well and suddenly I was 5-2 down,” Van Veen said.
“Last week, when I beat Kevin Doets, that’s where I felt most at ease on the stage in recent times.
“It’s been difficult the last couple of months. I need to work hard for it, but I’m still here and winning games and that’s what it’s all about.”
Joyce also came through a deciding leg, edging past Germany’s Martin Schindler in front of a partisan home crowd. His reward is a last-16 tie against Niko Springer, who ended Ross Smith’s title defence with a 6-3 win.
Earlier, Nijman avenged last week’s defeat to Krzysztof Ratajski with a convincing 6-2 triumph over the Polish number one. The ProTour leader averaged close to 100 and will now face Ryan Searle, who beat Dirk van Duijvenbode 6-4.
“I’ll take the 98 average,” Nijman said. “I’m feeling really confident and really relaxed, to be honest.
“Sometimes you’ll have these days where you feel like everything is going to go your way and today was one of those days.”
Elsewhere, Doets defeated Nathan Aspinall 6-3 to keep his hopes of a first European Tour title alive and set up a meeting with Justin Hood, who impressed in a 6-1 win over Jermaine Wattimena.
Cameron Menzies continued his recent resurgence with a 6-2 victory over Stephen Bunting, setting up a clash with Luke Woodhouse, while Jimmy van Schie's eye-catching European Tour debut continued with a 6-1 win over Mike De Decker.
Sebastian Bialecki bettered Chris Dobey to reach the last 16, where he will face Van Schie, while Damon Heta, William O’Connor, Ricky Evans and James Wade also progressed.
Results
Round two - afternoon
Wessel Nijman 6-1 Krzysztof Ratajski
Luke Woodhouse 6-3 Andrew Gilding
Jimmy van Schie 6-1 Mike De Decker
Ricky Evans 6-3 Daryl Gurney
Damon Heta 6-4 Karel Sedlacek
Ryan Searle 6-4 Dirk van Duijvenbode
Dave Chisnall 6-4 Joe Cullen
Justin Hood 6-1 Jermaine Wattimena
Round two - evening
William O’Connor 6-2 Danny Noppert
Sebastian Bialecki 6-3 Chris Dobey
James Wade 6-2 Niels Zonneveld
Cameron Menzies 6-2 Stephen Bunting
Kevin Doets 6-3 Nathan Aspinall
Gian van Veen 6-5 Dimitri Van den Bergh
Ryan Joyce 6-5 Martin Schindler
Niko Springer 6-2 Ross Smith