Vale's hero was goalkeeper Sam Johnson, making his debut, as he scored the final penalty against opposite number Karl Darlow, who had seen his penalty saved, in a mammoth shoot-out which contained a full total of 22 spot-kicks.
Walsall took the lead in the 25th minute when Richard Duffy handled the ball trying to stop Florent Cuvelier's dart into the box, and Cuvelier - on loan from Stoke - drove home the resulting penalty.
It looked all over when Will Grigg added a second for the Saddlers two minutes into the second half, setting up a commanding lead.
But just two minutes later Ryan Burge reduced the arrears for Vale before top scorer Tom Pope equalised with his 12th goal of the season after 61 minutes to force the penalty shoot-out drama, with Vale booking their place in the northern section quarter-finals.
