The result is a great testament to Town's youth system that has already produced the likes of Jamie Tolley and Dave Edwards.
Midfielder Eddie Hope was the only goalscorer in the 1-0 win. Town also had Jamie Haynes controversially sent off in the second half.
Town's run this season has seen them dispatch Burton and Mansfield's youth teams, and the side will be looking forward to the final.
Youth team boss Nigel Vaughan told ShrewsWeb: "It's been a great night and we deserved to get through and hopefully we can go and enjoy the final."