The Welshman found himself 3-0 down in the third round of Q School, but despite the trajectory of the game, he dug deep and rallied off the next three frames to sensationally take the match to a decider.
However, a break of 60 from Sargeant denied Walker what would have been a memorable fight back in Sheffield.
Walker recently claimed the seniors world championship crown following a string of comeback victories.
The 46-year-old produced turnarounds against Ken Doherty, David Lilley and Jimmy White as he stormed to the Crucible title.
Walker recently admitted that his decision to play at Q School was influenced by his father and Mark Williams. The Welshman also revealed this could be his last attempt at making the professional tour, should he fail to progress.
The player will now turn his attention to the last two remaining Q School events, starting with a second-round clash against Fergal Quinn on Monday.
Elsewhere at Q School
After knocking out the world seniors champion, Sargeant went on to pick up a 4-2 victory over Harvey Chandler to seal his place in the final round of Q School.
The 24-year-old will now take on former world number 20 Rod Lawler, with the winner going on to claim the tour card.
Lawler enjoyed a 4-1 win over Lukas Kleckers, with the German now turning his focus on the last remaining two Q School events if he is to make an immediate return onto the professional circuit.
Fergal O'Brien, who is also looking to bounce straight back onto the pro tour, will take on Rory McLeod in a huge clash between two very experienced campaigners.
Alex Simmonds is the third English player in the final round of Q School, and he will face Hong Kong's Lee Chun Wai Andy.
The fourth clash in the final round will see Akani Songsermsawad go up against Bai Langning.