Selby, who posted a maximum 147 break during his win against Jack Lisowski on Thursday, recorded two more centuries.
But he met his match in Allen, who followed up a 143 break in frame three by closing out the contest with a run of 126.
Allen is chasing the seventh title of his professional career, and he installed himself as clear favourite by knocking out Selby a day after eliminating Judd Trump.
Robbie Williams, meanwhile, reached the last four of a ranking event for the third time following a 5-1 success against China's Lyu Hoatian in Milton Keynes.
Ryan Day moved into the semi-finals with a 5-4 victory over Yuan Sijun, clinching the deciding frame with a 124 clearance.
But there was no joy for Day's fellow Welshman Jamie Jones, who bowed out 5-3 against Noppon Saengkham. The Thai player tackles Allen in Saturday's first semi-final.