The world number one averaged a staggering 108.55 - the third-highest ever recorded in a Grand Slam second round match - in a performance that combined ruthless precision with remarkable resilience.
It was an exhibition of control and focus from a player who continues to elevate his game beyond the reach of most opponents.
Humphries stormed to a 5-0 lead, averaging over 119 after the opening five legs.
The highlight came in a ten-dart leg that saw him take out the traditional nine-dart route of 141 before finishing on tops.
Van der Velde offered resistance with a superb 164 checkout, but Humphries was unrelenting, closing the contest 10-3 with a 77 per cent checkout success rate.
"It was probably one of the best performances I've ever had in my life," Humphries told Sky Sports after the match.
"I woke up this morning and couldn't get my head off the pillow.
"I've had a bad neck for a few days. It's been a struggle for me all day. It's crazy how you can perform like that with an injury I've had to deal with.
"I cannot believe I've done that. I'm in a lot of pain now, it's hurting me, but I'm a fighter. I put everything on the line tonight."
Next, Humphries will face Michael Smith, who survived a chaotic encounter with Chris Dobey, eventually edging through 10-9 after a nerve-jangling series of missed match darts.
Between them, the pair squandered twenty opportunities to win before Smith finally pinned double four.
Elsewhere, Gerwyn Price overcame Martin Schindler 10-6 to continue his fine record in the competition, and Ricky Evans battled past Luke Woodhouse 10-9 to reach his first-ever Grand Slam quarter-final.
Yet the night belonged to Humphries, who now looks like the player to beat in Wolverhampton.