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Three first-half goals from Abdul Fatawu, Emmanuel Gyamfi and Martin Antwi ensured the Zambians suffered their second defeat in the competition.
Kotoko made their intentions known right from the blast of the referee Joshua Bondo's whistle as Abdul Fatawu opened the floodgate for his side. He hit a free kick into the near post from the edge of the penalty box.
Yacouba failed to increase the lead for the Reds after he got better of his marker from inside the penalty box but he shot across the face of goal.
Debutant Daniel Darkwah resurging run from the left flank helped Kotoko to double the lead in the 22nd-minute mark. His powerful shot was pelted by goalkeeper Allan Chibwe that allowed Emmanuel Gyamfi to poke home into an empty amid a stiff from three opponent players.
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Coach Akonnor was forced to replace Gyamfi with Kwame Boahene after the former got injured while scoring the second goal.
The piled more pressure on the Zambians and their effort was rewarded when Martin Antwi hit a freekick into the top right corner of the far post.
Nkana's coach Beston Chambeshi replaced goalkeeper Allam Chibwe with Kelvin Malunga after conceding the third goal.
Nkana piled more man forward after the recess but Kotoko held on tight to their attacks.
Nkana threw caution to the wind in the dying embers of the game to get a respectable scoreline but the effort as too little too late as referee Joshua Bondo brought proceedings to an end.