It took 17 penalties to decide the tie after an exciting 3-3 draw had proceeded the shootout.
Luke Fedorenko fired Barnsley in front after 13 minutes but strikes from Alex Fleeting and Carl Ashton gave Derby a 2-1 half-time advantage.
But Barnsley came out all guns blazing for the second half and the lethal Fedorenko put The Reds level on 63minutes.
There were then scene of delight in the very last minute of extra time when Jacob White looked to have sent Barnsley through when he made the score 3-2.
But incredibly in injury time Derby drew level
The Reds then managed to net nine of thier 10 penalties and when James Waggett made a decisive save, Ryan Jennings stepped up to keep ensure one Barnsley side still had thier Cup dreams intact.
Simon Davey told www.barnsleyfc.co.uk:
"It was an excellent performance, an excellent display and an outstanding result for the youngsters, the Academy staff and for the club as a whole. Simon and the rest of the first team staff we all watching and were delighted with what they saw on the night.
"It was a fantastic evening for Barnsley Football Club".