Afriyie opened the scoring in the 11th minute with a rebound shot from close range after goalkeeper, Appiah-Kubi saved Ibrahim Salifu's shot.
With a few minutes to the break, after Lions' were reduced to ten men as Abdul Rashid was sent off for a reckless tackle on Kwadwo Obeng Jnr.
Having the numerical advantage, the Phobians made it count as they doubled their lead in the second half.
A defense splitting pass from Salifu Ibrahim saw Isaac Agyenim Boateng score his first goal of the season for the Phobians.
Hearts of Oak pushed for more and they rightly got it when Sulley Muntari connected a cross from a corner kick to Afriyie Barnieh who headed it home to make it 3-0.
Hearts of Oak climbed to the fourth position on the Ghana Premier League table after their win.