Trying to clear a long throw-in into the danger area from Jack Robinson, Wiseman could not sufficiently clear the ball and it bounced across the line off the bar.
Having won their opening league game of the season 3-1 at Doncaster, Blackpool failed to fire for much of the game and despite not having managed to score so far this term, Barnsley just about enjoyed the better of the first half at Bloomfield Road.
Their best chance of the half came in just the fourth minute.
Midfielder David Perkins played an expertly-executed one-two with striker Chris O’Grady before lashing a super drive inches over the bar.
O’Grady himself was next to go close. The former Sheffield Wednesday striker picked up a smart pass from Tomasz Cywka before driving a low shot narrowly wide.
Bobby Grant saw a couple of efforts blocked for Blackpool, but it was not until the 42nd minute that he hosts went agonisingly close to breaking the deadlock.
Kirk Broadfoot played Michael Chopra in behind the Barnsley defence, only for the former Newcastle and Cardiff hit-man to screw a low, angled strike just past the far post.
Barnsley got the second half off to a flying start as they almost broke the deadlock a minute after the resumption.
Full-back Scott Golbourne found acres of space down the flank and crossed for O’Grady, only for the big striker to guide a header dismally over the top from barely eight yards.
The next Tykes chance fell to Cywka, who took a short free-kick from Jim O’Brien before lashing in a shot which nestled in the side-netting.
Blackpool just could not find a foothold, though substitute Nathan Eccleston pounced on a loose ball before sneaking past O’Brien and firing a low drive narrowly wide.
At the other end Barnsley were still looking slightly the more likely to open the scoring, and supersub Jason Scotland missed a golden opportunity.
Leaping highest to meet another measured Golbourne cross, Scotland could only guide a header wide of the mark with Matthew Gilks left rooted to his line.
With the game looking like it would end goalless disaster stuck for the away side.
It was back to basics for Ince’s men as a long-throw in to the box caused chaos and Wiseman was the unlucky victim as he miscued in to his own net.