Promising 20-year-old Prizmic, ranked 87th, secured his first-ever win over a top-10 player in a three-hour battle in the Spanish capital.
American Shelton triumphed at the Munich Open on Sunday on clay but was unable to force a single break point on Prizmic's serve.
Earlier, Italian Lorenzo Musetti, ranked ninth, defeated Hubert Hurkacz 6-4, 7-6(4), before his compatriot Jannik Sinner, world number one, was due to face France's Benjamin Bonzi.
Women's number two Elena Rybakina scraped into the Madrid Open third round with a 4-6, 6-3, 7-5 win over Elena-Gabriela Ruse.
Kazakhstan's Rybakina, who won the Australian Open in January and triumphed at Stuttgart last week, struggled in the first set, making 24 unforced errors to just eight winners.
After claiming a topsy-turvy second set, she came back from a break down in the third and sealed the victory on her third match point.
Rybakina will meet Zheng Qinwen, who produced a similarly battling performance to overcome Sofia Kenin, in the third round.
"Today, I basically survived," said Rybakina after her hard-fought victory.
"It wasn't the greatest performance but Gabriela, she played very well. She was playing very deep and aggressive, so it was very difficult.
"My serve was not really helping me today... but I'm really happy that I managed to win, and I hope I can bring better tennis next round."
Later on Friday, Coco Gauff takes on Leolia Jeanjean and Jessica Pegula faces Katie Boulter.
