The Reds are now unbeaten in five games and moved up a place to third-bottom, now in the relegation zone on goal difference.
The hosts forced Sami Radlinger into a string of good saves and hit the crossbar but the visitors also hit the post through Jacob Brown and had three goals ruled out for offside.
Gerhard Struber kept the same team that drew with West Brom on Thursday, after Alex Mowatt recovered from illness.
There were no chances in the first quarter of the match until Conor Chaplin headed a left-wing cross well off-target from 12 yards out. Chaplin then had a goal ruled out for offside after kicking in from a few yards out following Cauley Woodrow’s backheel from a Jordan Williams cross.
The Swans had offered very little going forward in the first half an hour but then suddenly had three chances in five minutes. First, after Williams failed to cut out a simple pass, Bersant Celina burst into the box from the left and had the first shot on target of the game which was blocked by the legs of Radlinger.
The goalkeeper made an even better save seconds later when a cross from the left was not cleared and Sam Surridge was free on the right of the six-yard box but Radlinger came up with an outstanding point blank stop.
Radlinger almost cost his team a goal soon after when he raced out of his box to head away a long ball but it went straight to a Swansea man and Surridge shot from 35 yards but it lofted onto the bar.
The Reds had a huge chance to take the lead early in the second half when Mowatt’s low cross from the left took a slight deflection and reached Brown at the far post three yards out but he slammed his effort against the post.
At the other end, Radlinger made another save from an Andre Ayew header then Celina put the rebound well over with the goal gaping.
Struber made a double change after an hour with Mike Bahre and Patrick Schmidt coming on for Mowatt and Brown. Both Schmidt and Chaplin put the ball in the net but were each given offside as they went through on goal, with the same happening at the other end to Surridge.
Swansea substitute George Byers and Barnsley’s Luke Thomas each fired wide of the bottom right corner from just outside the box. Woodrow’s effort from a similar distance was straight at the goalkeeper then Celina drew a save out of Radlinger who had to dive to his right to push away the 25-yard effort.
Barnsley (4-4-2 diamond): Radlinger; J Williams, Diaby, Andersen, Ouder; Halme, Mowatt (Bahre 61mins), Thomas, Woodrow; Chaplin, Brown (Schmidt 61). Unused: Collins, Sibbick, Dougall, Simoes, Styles. Yellow cards: Mowatt, Andersen, Diaby.
Swansea (4-3-3): Woodman; Naughton, Cabango, Wilmot, Bidwell; Carroll (Byers 70mins), Grimes, Fulton; Celina, Surridge (Routledge 77), Ayew. Unused: Nordfeldt, John, McKay, Baston, Roberts. Yellow cards: Carroll.
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