Chasetown defeated League One Port Vale to book their place in the third round.
Luke Rodgers put Port Vale in front in their first tie but Chasetown would not be denied and Mark Branch equalised with a 40-yard free-kick.
In the replay at the Scholars Ground Rodgers missed two penalties for Vale and the match looked to be heading for extra-time before the decisive 89th-minute winner.
Chasetown substitute Smith struck with a header, much to the delight of the 1,986 packed inside the ground. Mass celebrations followed the final whistle.
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