Bjorn Sigurdarson and Kevin Foley both blazed their spot-kicks over the crossbar before James Henry was denied by goalkeeper Fabian Spiess as County triumphed 3-1 to secure a thoroughly deserved success.
The visitors were dominant throughout and really should have settled affairs well before the shootout as the tie finished goalless after 90 minutes.
But they could not find a way past goalkeeper Carl Ikeme, who continued the good form he had shown in Wanderers' 3-0 win at Colchester on Saturday.
Adam Coombes and Yoann Arquinn tested Ikeme in the opening 25 minutes before Jamal Campbell-Ryce and Mark Fotheringham both failed to hit the target when well placed.
Coombes was then denied again by Ikeme on the half-hour and at the start of the second half as a Wolves struggled to make any kind of impact.
When County skipper Dean Leacock headed wide in the 55th minute, Chris Kiwomya's side must have sensed it would not be their night.
Wolves did produce a late rally when Leigh Griffiths fired a free-kick into the side-netting but County eventually gained their just rewards as Wolves wilted in the shootout.