Blyth took the lead in the first half through Scott Emerson with Lewis Guy equalising on the hour mark.
With 89 minutes Newcastle were awarded a penalty when the referee adjudged that Justin Keegan had fouled Calvin Zola Makongo.
Zola fired the spot kick past Blyth keeper Phil Naisbett, before Martin Brittain added a late third to seal the win.
We now face Whitley Bay in the final, with the date and venue to be confirmed.