Defender Jody Craddock blasted their seventh spot-kick over the bar and into the visiting fans to give the League One club a victory they deserved on the night.
Chesterfield were the better side during normal time and would have beaten the Championship outfit without the drama of a shootout, but for visiting goalkeeper Carl Ikeme.
He made several excellent saves, but Wolves were disappointing in the final third and created few clear chances.
Manager Mick McCarthy made six changes for this first-round match, but he would still have expected a more fluent performance from his team, particularly in a disappointing first half which was short on talking points.
The final pass was often woeful, although Chesterfield almost shocked the visitors on the stroke of half-time when Colin Larkin cut in from the left and shot just wide.
The striker was a constant threat to Wolves and Chesterfield almost went in front in the 56th minute when Paul Hall's shot from ten yards was saved by the keeper's legs.
That stung Wolves into a response, and Rohan Ricketts got in behind the Chesterfield defence on the left and almost squeezed a shot between Barry Roche and his near post.
But Chesterfield were still looking the sharper team and, in the 70th minute, Larkin broke clear down the Wolves right and crossed for Derek Niven whose header was superbly saved by Ikeme diving to his right.
But Ikeme was fortunate six minutes from the end of normal time when a Mark Allott free-kick clipped at the edge of the wall and was just inches wide with the goalkeeper stranded.
The first period of extra-time was tame by comparison, but conditions had now become extremely difficult with torrential rain leaving surface water on the pitch.
Wolves almost snatched the game in the final minutes of extra-time but that would have been harsh on Chesterfield, and the tie went to penalties.
Both teams scored with their first two kicks but Wolves had the advantage when the Spireites' Alex Bailey missed.
Karl Henry had the chance to win it with Wolves' fifth kick, but Roche saved to his left to set up sudden death, where Craddock blazed over.