Allies took the lead in the 12th minute through Alex Aso.
Three minutes later the Capelli Boys nearly doubled their lead in as Victorien Adebayor’s effort was tipped over the bar by goalkeeper Ernest Sowah.
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Ten minutes from the break, Hearts were denied the leveller when goalkeeper Saed Salfu saved Malik Akowuah's shot.
Inter Allies went into the break with the slim lead and in the 68th minute double their lead through Adebayor.
With a quarter of an hour left, the Phobians got a consolation through Tony Quayson.