A sudden-death miss by Gordon Greer earned Wolves their victory when he crashed his spot-kick against the post.
It summed up the frustration for Swindon, who had hit the woodwork three times in the opening 90 minutes against a lacklustre Wolves side.
Wolves boss Mick McCarthy had called on his shadow squad for the tie and they struggled to get past the challenge of League One Swindon.
Andrew Surman, David Jones, David Edwards, Andy Keogh and Sam Vokes were all on target with Wolves first five penalties, but Callum Kennedy, Mark Mason, Craig Easton, Lloyd Macklin and David Lucas also converted their spot-kicks to take the shootout into sudden death.
Neill Collins struck for Wolves before Greer saw his spot-kick crash off the post to end Swindon's hopes of a giantkilling.
Wolves only really impressed in the opening stages when they enjoyed enough domination to take control of the match, but ultimately they were grateful to the woodwork for going into the interval on level terms.
After Kevin Doyle and George Elokobi had gone close, it was teenage Wolves debutant Nathaniel Mendez-Laing who started to run the show.
The 17-year-old was twice denied by smart saves from David Lucas - his first effort in the 16th minute being palmed over the bar.
But having managed to weather that storm, Swindon were unlucky not to take control.
Lively winger Anthony McNamee was the first to be denied by the woodwork when his 37th minute 25-yard drive crashed off the top of the bar.
Then the post and the linesman's flag denied Swindon the lead when Billy Paynter was adjudged to be offside when he turned home the rebound after Temitope Obadeyi had hit the post on the stroke of half-time.
Wolves were unable to find the same impetus with which they had started the game and barely threatened in the second period when they again were rescued by the woodwork.
After Collins had failed to test Lucas with a close-range header, Mark Marshall rattled the bottom of the Wolves post with a low drive that left goalkeeper Marcus Hahnemann rooted to his line.
Lucas then ensured that the game would be decided by penalties by denying substitutes Edwards and Keogh.