Home captain Michael Jackson and striker Keigan Parker missed from the spot while the visitors scored all four of their attempts.
Blackpool had dominated the first half of normal time before a double penalty award sparked the game into life early in the second half.
Jackson was controversially adjudged to have brought down Tommy Wright in the 50th minute and Wright took the spot-kick himself only for it to be brilliantly saved by Rhys Evans.
Two minutes later Ian Evatt handled in the Blackpool penalty area and Robbie Williams beat Evans from 12 yards.
In the 70th minute Scott Vernon scored with a great header from a David Fox free-kick to level the scores. In extra time Barnsley looked to have sealed victory with a Martin Devaney goal on 116 minutes but with a minute left Vernon grabbed his second with a magnificent volley into the roof of the net.