Tykes goalkeeper Nick Colgan tripped Warren Feeney in the box, the Irish striker scored one spot-kick and then saw one saved, before finally seeing his third effort hit the back of the net to see struggling Stockport earn a point.
Stockport boss Chris Turner amazingly made seven changes to the starting line-up following last week's defeat at Luton, and his faith in the new men paid early dividends when Barnsley skipper Tony Vaughan failed to clear sufficiently under pressure from Warren Feeney and the loose ball fell to Keith Briggs who fired home after just five minutes.
Feeney then went close with a looping shot which flew just over, before youngster Chris Williams volleyed wide as County looked revitalised.
The home side kept up the early pressure and Feeney almost poked the ball past Colgan after latching on to a long ball from Ashley Williams.
Barnsley finally showed signs of life just before the half-hour mark. From a corner-kick Antony Kay fired in a left-foot shot, Michael Chopra helped the ball on from close range only for Stockport goalkeeper James Spencer to pull of an excellent save.
Paul Hart's side then got their equaliser on 32 minutes as Michael Boulding raced down the left, side-stepped Jim Goodwin and then planted home a low shot from 10 yards.
After the break, Boulding again showed his pace down the left, this time leaving Stockport debut boy Joe Dolan for dead before rifling a shot disappointingly straight at Spencer.
At the other end Feeney almost punished a mistake by Kay, but the Irish striker's shot was well saved down low by Colgan.
Despite a good spell from Stockport, though, it was Barnsley who took the lead on 63 minutes. From Stephen McPhail's corner Vaughan smashed a shot straight at defender Williams, but from the rebound the big man made no mistake from eight yards.
Barnsley, and especially Chris Shuker, could well have sealed victory well before the end, but that late dramatic spot-kick ensured the visitors went home with just the one point instead of three.