McLeod - the oldest player at the Crucible Theatre aged 46 from Wellingborough - was 1,000-1 for the title before the tournament began, and recovered from trailing 4-0 to win 10 of the next 14 frames in what was the biggest win of his 26-year career.
McLeod will face Scotland's Stephen Maguire over the best-of-25 frames in the last 16 for a quarter-final place.
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"It's brilliant. I was relaxed at 4-0. He was potting everything. There is not much you can do so you have to bide your time," said McLeod on the BBC.
"Maybe I went into zombie mode because I didn't know the score..if it was 4-4 or 5-4.
"I tried not to think about things too much. You have to dismiss the pressure."
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Trump - world number two and 4-1 pre-tournament favourite alongside defending champion Mark Selby arriving in Sheffield - had appeared to be struggling with a shoulder injury as he resumed 5-4 behind on Wednesday morning.
He faces a small fine from World Snooker for failing to speak to the media afterwards. Understandable given the circumstances, but McLeod believes the shoulder injury cannot be used as an excuse for Trump again coming up short.
"He was 4-0 up and he didn't look that injured, so what can I do?" said the man nicknamed 'The Highlander' after the lead character from the 1980s film.
"I had to deal with holding myself together. I am the oldest player left in the tournament. At 46 you have your aches and pains.
"Age is just a number; it's how you look after yourself and I think I am doing OK."
Despite the injury that caused Trump to visibly wince on certain shots, this is still a huge disappointment for the sport's most attacking player, who has reached five finals this season, winning two of them at the European Masters and Players Championship.
Judd Trump is out in the first round in Sheffield.
Image credit: Eurosport
Bristol's Trump made only three breaks over 50 in 18 frames, his highest being a 65 in the 12th frame as his form deserted him at the key time. McLeod's tactical game eventually held sway with 72, 77 and 66 his best efforts in a gruelling encounter that required a third unscheduled session at 9pm on Wednesday evening.
The players were forced to reappear for failing to complete the match in the allocated time in the morning session with McLeod slowly extending his lead to 9-7 against an opponent blighted by inconsistency over six hours and 44 minutes of exacting snoooker.
Trump - who lost the 2011 world final to John Higgins - kept his hopes flickering by winning the first frame of the restart, but McLeod held himself superbly well to claim the 18th frame at the second attempt after another Trump error in missing a mid-range red proved to be his final shot of the match.
Selby has been installed as 3-1 tournament favourite with Ronnie O'Sullivan second favourite at 4-1 for the £375,000 first prize. McLeod's odds unsurprisingly have tumbled to 100/1 after his unexpected success.
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