The five-time World Champion Van Barneveld put on a clinical display, hitting six doubles from ten attempts.
The 55-year-old punished nine missed doubles from White during the contest, and finished with a flourish as legs of 13 and 11 darts sealed the win.
Van Barneveld has now set up a darting date with reigning World Champion Wright in a highlight of Saturday's second round fixtures.
"I'm happy with the win and looking forward to tomorrow," said Van Barneveld. "I love to play Peter - I love him to bits, but tomorrow it's my stage.
"We all know what he can do, but he's struggling sometimes and if I play my good game I can beat him - but I have to play really well tomorrow."
He added: "The first two or three legs were a bit dodgy but fortunately I won those, and then you see Ian struggling. Ian wasn't playing his game, but I'm happy to beat him."
Geert Nentjes and Danny van Trijp were other Dutchmen to enjoy 6-0 wins in Friday's first round as they also progressed to the second round of the PDC European Tour event, where they meet Krzysztof Ratajski and Martin Schindler respectively.
Nentjes averaged 98 and finished six doubles from ten attempts to whitewash Josh Rock - a quarter-finalist last weekend in the Hungarian Darts Trophy - while Van Trijp was too strong for John Henderson.