Breaks of 96 and 69 saw Trump move within one of the final, but Wilson kept eating away at the deficit before a break of 72 sealed victory.
Trump was in total control at 5-2 and was at the table in the deciding frame, but a reckless attempt at a plant allowed his opponent back to the table and Wilson needed no second invitation.
It was a brave, attacking display from Wilson, whose sole ranking success so far came at the Shanghai Masters - where he edged Trump 10-9 in the final.
Now, he'll face Mark Allen for this illustrious title having looked set to bow out before launching one of the most remarkable comebacks in the tournament's storied history.
For Trump, who has yet to reach the Masters final having also lost at this stage six years ago, this was a damaging defeat in a career which many assumed would have produced many more triple crown titles than a sole triumph in the UK Championship way back in 2011.
Wilson took inspiration from the late Paul Hunter - winner of the Masters title three times between 2001 and 2004 when it was played at Wembley Conference Centre - to produce his stirring recovery.
Hunter was famous for his Masters fightbacks, and Wilson came up with one of his own.
"People keep calling me 'The Warrior' and I thought to myself, 'I haven't won a comeback in years, I'm going to stick in there and, this venue, funny things can happen here'," Wilson said on BBC Two.
"The late, great Paul Hunter made some awesome comebacks and I was thinking of him a little bit and trying to draw a little bit of inspiration from some of the comebacks he made and I just managed to stick in there."
Wilson felt he had been given an opportunity to spark a fightback after Trump "took a liberty" with a pot attempt when appearing well set to close out victory.
"It let me settle and I just needed one frame to get my arm going from 5-2 down to get back into the match," Wilson added.
"I just thought to myself, 'Right, I am going to go for it now', and when opportunities came I thought I just had to start taking them, whether taking a risk or not.
"I just started to grow in confidence and find my game."
Saturday's late match between Mark Allen and John Higgins was another high-quality encounter, with the former prevailing 6-3.
Both players produced some impressive breaks during the opening exchanges, with a clearance of 131 landing Scotland's Higgins the fifth as he reduced the deficit to 3-2.
Allen, though, responded with two half-century runs to move within a frame of the final.
A break of 127 gave Higgins, a two-time Masters champion, hope of extending the contest into the evening, but Allen produced another accomplished break of 75 to take his place in Sunday's final.
He said in his post-match television interview: "It (reaching the final) is good, but I came here to win the tournament."
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