Neath's 21-year-old White was just eight when Williams won the first of his world titles; and the following year the gifted potter entered the Guinness Book of Records as the youngest player ever to make a competitive century, after knocking in a 105 in a local league match.
In 2006, at 14, he became the youngest winner of the world amateur title. He struggled to make an impact in his early years on the pro tour, but has made a breakthrough this season, qualifying for the televised stages of four ranking events, and he is now through to the last 16 for the first time.
Despite being hauled back from 4-1 to 5-5, he played superbly in the closing stages against his experienced opponent. Breaks of 65 and 72 helped put him 8-5 ahead. Williams pulled one back by clearing from the penultimate red to the pink, but White finished brilliantly with runs of 90 and 96 to win the last two frames.
"It is hard to take it all in at the moment," said White, who won two matches to qualify. "It is an unbelievable place to come and I was really pleased with the way I coped with it all out there. To play that well and get a win against Mark is an unbelievable feeling.
"It is just something that you can dream of. So for me to actually do it, I cannot put it into words. I will be back on the practice table tomorrow and hopefully if I can put in another performance like that who knows what can happen.
"It means everything to me. I always looked up to Mark and it was a privilege to play him and to play as well as I did. I have always believed in myself and I knew that my game was good enough when I was 16 or 17 years old.
"I will just concentrate on the second round now. I am over the moon to have won that match but now I need to start getting ready for the next match."
Williams said: "He potted a lot of long ones and scored very heavily and probably out played me in every department. He was winning some frames in one visit and that's what you have got to do really. In some frames I had a bit a bad run of the ball but overall you cannot argue with that.
"He is one of the best young lads coming through. People mention Jack Lisowski but I think this kid could be even better. He got a century break as a nine-year-old in a competition whereas I didn't get one in practice until I was 13.
"He is still only 21 and if he can continue to play like that then he will be dangerous for anybody. I just hope that he goes and plays like that in the next match and does himself justice.
"For me it has been a season that I can't wait to forget. I will go back and have a couple of weeks off and try to get myself ready for next season."
Ball by ball scoring and results from tournaments