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Allen got off to a great start, punishing Wilson for missing a simple red to take the first frame with a break of 99.
The Englishman hit back however, with a break of 63 to level matters and the pair traded the next two frames as well to head into the interval all square.
Wilson then went to 5-3 ahead, after a break of 125 in the eighth frame and seemed assured of the win. However, the Northern Irishman hit back to take the match to a decider.
Allen, who lost to the Antrim player in the Masters final in January, recovered his composure, however, to build a break of 89 which was good enough to take the match.
He will now face O'Sullivan, who beat Shaun Murphy 6-3 in the other semi-final, in the showpiece event on Sunday.
Stages 19 & 21