The world champion racked up two centuries in the match to come back from 2-0 down but Walker played one of the matches of his life to earn a deserved victory over the reigning world champion.
The 43-year-old, who reached the quarter-finals of the World Championship as a teenager back in 1997, will now play Gary Wilson later on this evening for a place in the quarter-finals.
Walker could not have asked for a better opportunity to take an early lead when he got in among the balls with the table well set up for a frame-winning break, racking up 74 to take a 1-0 lead and he was in the balls again when Trump missed a long red to the left corner.
A circumspect player at the best of times, Walker took his time planning the opening pot but made it worth it, cashing in on the opportunity and making 67 courtesy of a fortuitous plant with a two-frame lead beckoning.
Tellingly, Trump still hadn't potted a ball and was given no opportunity to do so as the world No 80 knocked in the extra red to take him to within two frames of a major upset.
Trump had complained after both of his matches in Crawley that he had struggled to get into his rhythm and 42 minutes into the match, he had still not potted a ball.
The world champion eventually got his name on the scoreboard with a long red at the beginning of the third frame and despite the lack of table time, he appeared to be straight into his stride.
In a matter of minutes, he had his 20th century of the season under his belt and after a spectacular pink, sunk the black to make 135 and halve the deficit.
It was not long before the Englishman was level, knocking in a second century to wipe out the lead Walker had worked so hard to build.
He would be given a chance to take the lead again though as Trump took on a typically ambitious plant and missed, allowing his opponent to accumulate a break of 59, only to miss frame ball with the rest in his hand.
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But the world champion missed two reds, both of which he would have expected to sink, and Walker capitalised to take a 3-2 lead.
He was similarly ruthless a couple of minutes later after winning a safety battle and nervelessly rolling in a long red to give him the chance for the biggest win of his career.
Trump came back to the table with two snookers remaining and would not give up on his tournament life easily but Walker clung on to complete the upset.
ENGLISH OPEN ROUND THREE RESULTS
- Zhao Xintong 4 - 0 Neil Robertson
- Mei Xiwen 4 – 1 Elliot Slessor
- Gary Wilson 4 - 3 Joe Perry
- Barry Hawkins 4 – 2 Fergal O'Brien
- Thepchaiya Un-Nooh 4 – 2 Graeme Dott
- Ronnie O'Sullivan 4 – 1 Hossein Vafaei
- Shaun Murphy 4 – 0 Fan Zhengyi
- Mark Allen 4 - 1 Louis Heathcote
- Tian Pengfei 4 – 2 Dominic Dale
- Ricky Walden 4 – 3 Michael Holt
- David B Gilbert 4 – 2 Kurt Maflin
- Xiao Guodong 4 – 3 Jack Lisowski
- Mark Selby 4 – 2 Matthew Selt
- Tom Ford 4 – 2 Kyren Wilson
- Si Jiahui 4 – 0 Zhou Yuelong