Jim O'Brien gave the visitors the lead against the run of play, midway through the first half.
The home side started the match on the front foot and nearly took the lead through Gary Taylor-Fletcher in the eighth minute, but his header was cleared off the line from a corner.
The Tangerines had another great chance after 17 minutes, when Chris Basham found himself unmarked at the far post from a corner but he failed to get his effort on target.
Barnsley started to build a bit of momentum, and came close through a O'Brien free kick that forced Matt Gilks into making a good save.
The away side then went in front on the 25-minute mark, when they hit Blackpool on the counter-attack from a corner and O'Brien slotted home a tidy finish to put Barnsley ahead.
Barnsley nearly doubled their lead nine minutes later, but David Perkins drilled his effort just over the bar from a corner.