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The Pohobians despite dominating the first half of the game failed to take most of the chances, with the likes of Joseph Esso, Fatau Mohammed being the worst culprits.
However, Kwadwo Obeng gave them the lead in the first 45 minutes.
But as the game was ending 1-0 in favour of the Phobians, Joshua Jesse scored an injury-time equaliser for Unistar to send the game into penalty shootouts.
The two teams were perfect from their first four penalties but Aminu Alhassan's spot kick and the Phobians fifth was well saved by Unistar goalkeeper Peter Onyame to send the Unistar into the quarterfinals.
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Elsewhere full-back Augustine Sefa scored the match winner to hand Asante Kotoko a 2-1 win over Nkoranza Warriors.
Sefa’s goal came in in injury time to enable the Porcupine Warriors to overcome a scare from the lower division outfit.
While Ashanti Gold edged out New Edubiase with a 2-1 victory at the Obuasi Len Clay Sports Stadium.
Full results of round 16 matches
AshantiGold 2-1 New Edubiase
Medeama 0-0 Samartex (9-8 pk)
Kotoko 2-1 Nkoranza Warriors
Berekum Arsenals 3-2 BA United
Liberty Professionals 0-0 Proud United (2-4pk)
Hearts of Oak 1-1 UniStar Academy (4-5 pk)
Heart of Lions 2-0 Kotoku Royals
Nzema Kotoko 3-0 Vision FC
QUARTER-FINAL PAIRINGS
Asante Kotoko v Berekum Arsenals
Ashanti Gold v Medeama
Proud United v UniStar United
Hearts of Lions v Nzema Kotoko