The world number 81 partially bankrolls his sporting dream by cleaning tables at a snooker centre, but has now scooped a minimum £20,000 prize for reaching the quarter-finals.
Grace reeled off five of the opening six frames, setting the tone with a match-high break of 84 en route to his impressive victory.
Neil Robertson wins second UK title boosted by stunning 147 break
"Every match I play here is the biggest of my career," said Grace afterwards.
"I’ve been around a long time and done nothing so I was due a run. I was a bit lucky in the first few frames today, I fluked a few balls. That’s what happens when you’re having a good week.
A week ago I was playing my first match trying to win £4,000, now I’m on £20,000. Events like these can change your life very quickly, I’ve just not done it before now. And hopefully I’m not finished yet.
He will contest a semi-final spot with either Martin Gould or Joe Swail.
Former champion Shaun Murphy went out of the tournament against Marco Fu of Hong Kong, the 2008 winner going down 6-4 in a contest in which he never quite hit his stride.
Mark Selby found life easier as he raced through his encounter with Dechawat Poomjaeng 6-1.
Selby swerved an upset against Jamie Jones in the previous round, eventually coming through 6-5, but never looked in trouble as he notched half centuries in the first five frames – breaks of 82, 58, 106, 86 and 98.
"I should have been put out of the tournament by Jamie the other night," said Selby.
"But having come through that match I’m feeling less pressure, and today I was relaxed and played my own, game.
If I get to the semi-finals I’ll be in the home stretch and starting to focus on the title. But I’ve got another tough match before that.
Latest results and order of play
1pm (UK time)
Peter Ebdon 2-6 David Grace
Dechawat Poomjaeng 1-6 Mark Selby
Marco Fu 6-4 Shaun Murphy
Luca Brecel 3-5 Matthew Selt
Thursday (best of 11 frames)
Liang Wenbo v Tom Ford
Neil Robertson v Stephen Maguire
Martin Gould v Joe Swail
Jamie Burnett v John Higgins
Robertson whitewashes Selby to set up final meeting with Liang Wenbo
Robertson weathers late Higgins charge