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Barnsley had the better of the possession in a poor first half but failed to take advantage.
Adam Hammill found space on the left for the home side and did well to send in an accurate cross that was aimed at striker Jon Macken but Stephen Crainey nipped in smartly and stretched to provide a vital defensive header.
From the resulting corner Carl Dickinson rose above the rest and powered a header wide when he should have found the target.
Twice Filipe Teixeira menaced using his trickery and guile down the left flank but, when he cut inside and lashed in a long-range effort, it was wide of the target. Soon afterwards another low raking shot was off the mark.
Barnsley might have profited from a Bobby Hassell free-kick before the break when Jon Macken grazed a header but Ryan Shotton's flick took the ball away and no one was on hand to finish off.
Teixeira fired another fierce shot into a crowded penalty area that ricocheted out, and when Dickinson smashed a free-kick from outside the area, Matt Gilks in the Blackpool goal made a comfortable safe from the first shot on target of the match.
At the other end Charlie Adam curled a free-kick from outside the area but Dickinson was on hand to head away the effort.
Only a super reaction save from Gilks at the start of the second half denied Barnsley the lead when the keeper stuck out a leg to force away Hammill's fierce low shot and Blackpool scrambled away the danger.
Blackpool produced their first real effort after 62 minutes when Adam slipped the ball to Keith Southern but his tame shot was wide.
But after 75 minutes Hume found the net when Macken chested Hassell's free-kick into the path of the substitute who finished with an angled shot.