Wassaman beat second-tier side Inter Allies 4-3 on penalties to book a quarter-final place in the MTN Ghana FA Cup.
Both sides failed to find the back of the net in regulation time at the Tema Park on Wednesday.
Goalkeeper Stephen Ahorlu saved Emmanuel Adjetey’s spot-kick which was Inter Allies’s fifth on the afternoon.
Inter Allies’s Hassan Williams crashed the first penalty-kick to the cross-bar despite displacing Ahorlu.
Wassaman will go on to face Tema Youth-who defeated Liberty Professionals at the Tema Park.
The League title has eluded them since their triumph in 1970.