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The dimunitive striker connected home from a cross to hand Maxwell Konadu's side victory over the arch-rivals which is a major boost for them ahead of the upcoming 2019/20 Ghana Premier League.
The results see Maxwell Konadu clinched his first trophy on his comeback.
Hearts took the lead after Kototo defender Empem Dacosta handled the ball inside the box and the burly striker drilled home from 12 yards.
Goalkeeper Kwame Baah got the direction of Kordji's kick, but he was some seconds late in pulling a save.
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Kotoko kept their heads high and continued pushing for the leveller and just on the nick of half-time, the scoreline was even.
Patrick Yeboah raided the left side of Kotoko attack and whipped in a left-footed cross which directed into the Hearts of Oak by defender Mohammed Alhassan as he attempted to clear his lines.
Yeboah again was involved in the clincher after whipping in a cross which met the head of Keita to bead Richard Atta in the post after 64 minutes.
On 79 minutes, Keita came close again but his header struck the upright after Christopher Nettey had delivered a prosaic cross.
Hearts of Oak had to finish the game with ten men after defender Robert Addo was sent off for a second yellow card offence after taking out Emmanuel Gyamfi who had to be replaced by Douglas Owusu Ansah.