Mechanics bowed out of the Macron Cup after a dramatic finale brought three goals in the last 10 minutes.
The hosts started as favourites in this third-round tie against the bottom team in North West Counties League first division south and Mechs attacked early on.
Both sides struck the woodwork in the early stages, AFC hitting the bar before Rangers struck a post from a free-kick.
The hosts had the final chance of the half, firing over from a free-kick, and the tie remained deadlocked until the 80th minute.
It was the Shropshire side who took the lead, George Taylor getting the final touch from a free-kick.
Blackpool were back on terms five minutes later, when substitute en Duffield equalised, but the visitors would have the final say in the 87th minute.
It was Daniel Howell who got on the end of the cross for the winner which earned Rangers a visit to Shelley in the quarter-finals.
Blackpool: Povey, Simmons, Dawson, McClean, Vaughan, Pickering, McKenna, Fishwick, Buchan, Thomas, Robinson; subs used: McGaragher, Bishop, Duffield.