Goals from Stephen Amankona and Isaac Oppong were enough for the Porcupines despite a strike from Philip Ofori.
The game was an outstanding fixture which was meant to be played on matchday one but Kotoko’s involvement in the CAF Champions League forced a postponement.
Kotoko head coach Seydou Zerbo maintained his starting XI which drew 1-1 with Hearts of Oak on Sunday.
The Porcupine Warriors opened the scoring against Nsoatreman in the 15th minute after Stephen Amankona converted a penalty kick.
Winger Isaac Oppong doubled the advantage just two minutes after the break after he was set up by Steven Mukwala.
Nsoatreman pulled one back in the 50th minute through Philip Ofori who got on the end of a corner kick.
Kotoko are now 9th on the league log with one more outstanding fixture left.
By Bill Eshun|3Sports|Ghana