The 55-year-old beat Raymond Smith 4-3.
King made the last eight for the first time at Alexandra Palace since reaching the semi-finals in 2009 met 'n 4-3 comeback victory over Raymond Smith.
The 55-year-old Englishman fought back from 2-0 en 3-1 down before seizing the advantage in the final set with a spectacular 124 checkout on the bullseye.
Australian Smith missed four darts at double top in the next leg and King capitalised to complete a final-set whitewash.
“I could feel the atmosphere building and building as I made my comeback,” King told Sky Sports.
“It was nice to be able to dig in and take advantage of it.
“I’ve got the game to make the final. It just depends if my proper game turns up.”
Luke Humphries reached his third quarter-final in four years with a 4-3 victory over Chris Dobey
Humphries had received a bye into the last 16 when Dave Chisnall tested positive for coronavirus.
Dobey soared into a 3-1 lead but Humphries turned the tide, with three ton-plus checkouts proving decisive.
“I got human at the end, my nerves kicked in,” said Humphries, who scored 177 to leave tops before missing match darts and finally finishing the job on double one.
“At the end my hand was shaking, my heart was going mad. Nerves got the better of me.
“It’s time for me to kick on now. The last two-quarter finals I was very new to the tour.
“But I’ve got more knowledge and experience now to go into the next game with more ambition to go further.”
Callan Rydz secured a quarter-final spot with a 4-1 victory over Alan Soutar.
Rydz recovered from losing his first set of the tournament to breeze into the last eight for the first time.