Aidian Collins gave Town the lead early in the first half before a goalmouth scramble in which goalkeeper Shane Supple appeared to be fouled led to Kevin Smith hitting home the equaliser from close range to put the teams back on level terms.
At full time the scores remained tied, and in the last minute of the second half of extra time England Under 16 international Daryl Knights popped up to head in Dean Bowditch's cross from six yards to send the blues into Tuesday's fourth round draw.