The Shropshire side took the lead with the first attack of the game. A defensive lapse let in Craig Ryan who finished a one on one past debutant Dale Reaney.
Chasetown’s efforts at goal in a flat first half were restricted to long range efforts including a couple from George Cater that flew over the crossbar.
The Scholars started the second half more brightly and earned an early corner which skipper Jimmy O’Neill fired a yard wide of the post.
Will Whieldon almost levelled against his old club with a dipping free kick that was clawed out by keeper Ash Rawlins.
Chase Substitute Jordan Flattley then clipped the top of the crossbar in the 75th minute as the hosts pushed for an equaliser.
Market Drayton clinched the tie 7 minutes from time. The visitors broke quickly and substitute Joe Cuff slotted the ball past Reaney.
Chasetown almost responded immediately with a superb diving save from Rawlins to deny Jake Lovatt.
Drayton killed the tie in the final minute of normal time. A corner kick was parried by Reaney and Andre James prodded home from underneath the crossbar.
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