Asante volleyed home from inside the area to give the Spireites the lead on nine minutes.
Luke Young equalised from the spot after Jak McCourt was harshly adjudged to have handled the ball.
But with the clock ticking down, Asante was put through on goal by Liam Mandeville and he slotted in the winner and his sixth in a Town shirt.
Here are Liam Norcliffe’s player ratings….
But with the clock ticking down, Asante was put through on goal by Liam Mandeville and he slotted in the winner and his sixth in a Town shirt.
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