Ian Harvey's close-range finish ensured Chippenham will get another crack at Conference North side Worcester.
An Adam Webster strike put Worcester ahead after veteran defender Des Lyttle had nodded Liam McDonnell's initial shot back into his path.
Chippenham equalised 60 seconds after the restart when the ball found its way to Harvey and he stabbed the ball in.
Webster struck the crossbar and Sam Wedgebury was also denied by the woodwork, but Chippenham held on.
Chippenham: Vaughan, Adams, Gary Thorne, McEntegart, Wayne Thorne, Allison, Harvey, Badman (Kirk 75), Herring, Constable (Simon Charity 81), Gilroy.
Subs Not Used: Griffin, Bunyard, Snoddy.
Goals: Constable 47.
Worcester: McDonnell, Lyttle, Thompson, Chris Smith, Warner, Wedgebury (Colley 82), Warmer, Hodnett (Hyde 59), McDonald, Webster, Kelly (Preece 90).
Subs Not Used: Clegg, Jones.
Booked: Kelly, McDonald, Chris Smith.
Goals: Webster 6.
Ref: P Gibbs (West Midlands).