The beleaguered Miners got off to a flying start in the game as they controlled possession and were awarded a penalty in the 17th minute by the centre referee after Emmanuel Osei Baffour was shoved in the box.
The silky midfielder elected himself to take the spot kick but he blasted the ball way off target.
AshantiGold continued to press the home side for the opener and they got their reward when midfielder Hans Kwoffie put them ahead with a fine finish on the 30th minute mark.
Asokwa Deportivo restored parity in the 81th minute through substitute Francis Arthur.
Both sides failed to add to their goals as the game travelled to penalty shootout.
The home side triumphed 3-1 in the shootouts to book a place in the next round of the competition.