English darts player Luke Littler. Photo: AFP
Littler, born 21 days after 56-year-old Van Barneveld won his last world title in 2007, hit nine 180's to overpower the veteran Dutchman.
The Englishman became the youngest player to reach the World Championship quarter-finals.
"Unbelievable! My average has shown it, my double percentage has shown it - I don't know what to say!", Littler told Sky Sports.
"He (Van Barneveld) said 'you can go all the way, I hope you can go all the way'. I said 'thank you' - he's a true gentleman and I respect Raymond."
Littler will play Northern Ireland's Brendan Dolan in the last eight.
-Reuters
