Burden, ranked 55, registered a 4-3 win to book his place in the last 16 of a ranking tournament for just the second time in his career.
"I should have won 4-2 but I haven't been in the big arena for a few years so I let the pressure get to me," said Burden.
"I thought I'd missed my chance so I was delighted to win it in one visit in the last frame. I beat John Higgins earlier in the season and in my book he's a better player than Judd, but in front of a packed crowd, to beat the world number one I'm over the moon. In best of sevens it doesn't really matter who you play, the top 50 or 60 in the world are all capable of beating each other.
"I've changed clubs and I'm practising a lot with Anthony Hamilton now which has helped me no end. He's such a knowledgeable player and I'm learning a lot from him. I'm enjoying it and wanting to go in and practise."
The 36-year-old now meets Ziao Guodong for a place in the quarter-finals after the Chinese comprehensively downed Graeme Dott 4-1.
Ding Junhui won a last-frame decider against Andrew Higginson in his first-round match.
Breaks of 57 and 71 helped Higginson move into a 3-1 lead, but with Ding needing to take all three remaining frames to survive, he did just that.
Starting with a 118 clearance for 2-3, Ding kept his opponent almost entirely off the table as he potted his way to frames six and seven to advance to the last-16 where he'll play either Robert Milkins or Anthony McGill.
Former four times world champion John Higgins produced some big-hitting snooker but nonetheless fell 4-2 to last year's Crucible runner-up Ali Carter.
Higgins began with a run to 59 only to allow 'The Captain' in to clear with 79, and after Higgins' 111 break levelled the match Carter was able to edge two frames for a 3-1 lead.
The Scot struck back with 83 but again dropped one on the final colours, sending Carter through where he will play Marco Fu or Mark Joyce next.
Rod Lawler was a 4-2 winner against Cao Yupeng in a low-scoring match.
The Chinese dominated the first frame before Lawler levelled at 1-1. He then took a two-frame advantage, including a break of 73 in frame four.
Cao hit back with a 70 to reduce the arrears by a frame, but Liverpool's Lawler saw the match out to set up a last-16 match against the winner of Ken Doherty versus Kurt Maflin.
They are the final match on Wednesday as the remaining five first-round matches are played at staggered times.
Lawler won the first professional title of his snooker career, after 22 years of trying, at the EPTC3 in September. He was runner-up in the 1994 Benson & Hedges Championship and 1996 International Open.
In a late-finishing match, Norway's Kurt Maflin beat home favourite Ken Doherty 4-2.
The Grand Finals, a ranking event, is the culmination of the PTC series of events held throughout the season.