The world number 21 won four of the last five frames for a 6-5 victory to reach the quarter-finals at the Barbican Centre.
Three-time champion Higgins, the fourth seed, held leads of 4-2 and 5-4 but King's battling qualities came to the fore as he levelled the match and forced a deciding frame, which he clinched with break of 69 - his highest of the match.
"There was a packed crowd in there and if you can't get yourself up for those matches, you might as well just pack up," King said on BBC Two.
"Even when I was behind I didn't really do anything wrong. He played two good snookers and I just missed them. It wasn't like I twitched on anything, he played some good shots and ended up winning.
"But I just felt really confident in myself and told myself to keep calm and stay confident. I felt comfortable and kept saying to myself just don't miss anything easy.
"I said that about 18 months ago I was playing to pay bills and now I'm not, I'm playing to enjoy and I'm working hard and I'm comfortable. It's not as if I need to pot this black because the mortgage hasn't been paid or whatever.
"Now I can play my game and relax and enjoy it. But it's about working hard and enjoying it."
Higgins is the latest big-name casualty to exit the competition after holder Mark Selby, Judd Trump and Ding Junhui all failed to progress, leaving 42-year-old five-time world champion Ronnie O'Sullivan as the highest-ranked player left in the tournament.
Asked if he felt he could lift the trophy, King said: "Let's not get too carried away. But I don't fear anybody. I've played Ronnie loads of times and I've done well against him.
"It isn't like years ago. When someone beat Stephen (Hendry) or Steve (Davis) people wondered how he'd been beaten but nowadays the strength in depth in our game is such that anyone in the top 60 in the world can, on their day, beat one of the top players."
In the other afternoon match, Stephen Maguire beat fellow Scot Graeme Dott 6-2 and he will now take on Joe Perry, who defeated Mark Allen 6-4 in the evening.
The other game on Thursday night was a really close-fought affair as Ryan Day produced a brilliant break of 138 in the deciding frame to edge past Li Hang 6-5.
WEDNESDAY DECEMBER 6
Afternoon Session (1300 GMT)
Fourth Round (Best of 11 frames)
TV Coverage: BBC/Eurosport
- Mark King 6-5 John Higgins (Match 116)
- Graeme Dott 2-6 Stephen Maguire (Match 117)
Evening Session (1900 GMT)
Fourth Round (Best of 11 frames)
TV Coverage: BBC/Eurosport
- Li Hang 5-6 Ryan Day (Match 113)
- Joe Perry 6-4 Mark Allen (Match 118)
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