The Welshman was forced to fight off an inspired comeback from Jose de Sousa in one of the best games ever seen at the Winter Gardens.
Price averaged 104.64 as he powered to a 16-14 victory in a captivating contest against his Portuguese rival.
The match got off to an explosive start as both men produced 160 checkouts, but it was the Iceman who edged in-front by taking a 3-2 lead.
The 37-year-old was averaging 12 points more than his opponent, yet De Sousa fired in a 93 checkout to level the match at 5-5.
Eventually, Price did establish some daylight as his big scores kept on coming. The Iceman moved 13-8 ahead and appeared to cruising to a semi-final spot.
However, the Special One had other ideas and produced a remarkable five-leg burst to sensationally level-up proceedings. His run included a 12-darter and a 100 checkout with two double tops.
Price stopped the rot and bagged consecutive 14-darters to move within one leg of the final four.
De Sousa prolonged the match with a 10-darter, but couldn't take the match to a tie-break after missing five darts at double in the next leg.
That enabled Price to wrap up a memorable Blackpool victory as he secured his semi-final clash against Danny Noppert.
The win also takes Price back to the top of the PDC's Order of Merit, ahead of current world champion Peter Wright.
"That was a difficult game," reflected the 2021 World Champion. "I played pretty well and I think I deserved to go through.
"Jose is a great player. He dug in right until the end, and I'm thankful to come through.
"I believe I'm the world number one, especially with performances like that. I think it's where I deserve to be."