Jon Maken and Jacob Butterfield were the Oakwell heroes, striking in an 18-minute spell as the Hillsborough side relaxed.
Wednesday almost snatched the lead on nine minutes, Marcus Tudgay heading the ball into the path of the incoming James O'Connor, whose left-foot strike was turned away in spectacular fashion by Luke Steele.
But the Barnsley keeper was helpless a minute later, veteran midfielder Michael Gray picking out Jermaine Johnson with a precise cross and the Jamaica international hammered in an unstoppable shot from close range.
The Tykes side hit back immediately, Anderson De Silva weaving his way into the area before lashing in a low strike, snatched at the second attempt by Lee Grant.
Barnsley should have been back on level terms minutes later, Macken was gifted a chance ten yards out, but his low strike hit Grant's outstretched leg as the ball spun wide of the target.
Macken had another shot blocked by Grant before Wednesday forged further ahead. Tommy Spurr's long throw caused problems, the ball grazing the top of centre-back Stephen Foster's head as Gray pounced with a brave diving header.
Simon Davey's side carved out another half chance, Macken was again the culprit, his shot cannoning off a defender before Johnson watched as his angled drive was deflected round the far post.
Barnsley were back in the game in the 58th minute, Martin Devaney's cross coming throw a crowd of players, as Butterfield finished with a low strike from 12 yards.
They added a second in the 76th minute to set up a nail-biting finish. Steele's free-kick was head on by Kayodi Odejayi and Macken steamed into the box to slam the ball wide of the advancing Grant.
Darren Potter almost won it for Wednesday in the dying minutes, his long-range strike being saved at the second attempt by Steele.