Allen, who rattled off three centuries in the first three frames on his way to an impressive 6-3 win over Mark Williams in the first round on Tuesday, started in similar fashion in the quarter-final.
He recorded breaks of 84, 63 and 75 to move 3-1 ahead after Wilson had taken the third frame.
Slip-ups from Allen allowed Wilson to draw level as he won the fifth and sixth frames, before errors from the Englishman gave the world number three the chance to re-establish his lead.
With momentum swinging back in his favour, Allen, who has won the Champion of Champions and Shootout events this season, would take back-to-back frames.
A miss on the black from the Northern Irishman saw Wilson claim the ninth frame and keep his hopes of progressing alive.
However, Allen’s superb 69 break in the final frame sealed the victory for the 38-year old.
