Dave Freeman had already hit the post for Sphinx when Vale took the lead through Martin Wayman who broke through to score with a low shot in the 7th minute.
Andrew Cooper struck the bar at the other end for Sphinx, who were level in the 12th miute thanks to an exquisite loft from Dave Freeman.
Both sides battled away before Andy Wilson King twice headed off the line with ten minutes of the opening period remaining.
The Birmingham based side came out fired up for the second half and were ahead sixty eight seconds into the half with a well take goal by Skinner.
Chad Dugan added a third in the 63rd minute for the visitors, but Steve Shea and Neil Moran's side stuck to their guns.
They were denied a clear goal in the 76th minute when a badly positioned referee could not see through a crowd of players that the ball was hooked back a yard over the line.
Craig Goodbody bundled the ball in from a corner three minutes later but Sphinx could not find a third goal and went out of the competition.