The debutansts held the Phobians to a goalless draw on match day 13 of the Ghana Premier League
Vincent Atingah put Hearts of Oak in the driving seat, but Ibrahim Bolga All Stars cancelled out the lead.
Hearts of Oak restored their lead through Thomas Abbey, the skipper for the Accra giants.
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Back from recess, the Bolga lads upped their play and in the process snatched the equaliser through Alhassan Rahim.
Rahim turned the scales in favour of the hosts when he sent them into the lead and with defeat staring on the faces of Hearts of Oak, Alexander Kouassi came to their rescue with the goal that handed a vital away point.