The unseeded South African landed seven 180s and averaged 92.25 as he stunned Steve West, the world number 22, 4-2.
It is only the second time Petersen, who will face Nathan Aspinall tomorrow, has reached the fourth round, but he said: “I was very confident.
“I have been in this situation before and I knew I had to play my best all the time.
“He missed his doubles and I took the chances I should have.
“I have always had it in the bag, talent wise, and it’s just about doing it on the big stage.”
Petersen averaged only 79.9 in the opening set which West claimed 3-0, but then won five of the next six legs, including checkouts of 139, 127 and 120, to go 2-1 ahead.
West levelled at two sets all, but Petersen held his throw to win the fifth in a deciding leg and go within one set of the match.
He broke West’s throw in the third leg and then finished on double-eight to win the tie, after West had missed five darts at double-top.