After City made the brighter start, it was the Tykes who took the lead 19 minutes in as Martin Devaney's cross in from the right was flicked on and Paul Hayes was given time at the far post to hammer home a low volley into the bottom of City keeper Willy Gueret's net.
Barnsley Win Through In Cardiff Cracker
After City made the brighter start, it was the Tykes who took the lead 19 minutes in as Martin Devaney's cross in from the right was flicked on and Paul Hayes was given time at the far post to hammer home a low volley into the bottom of City keeper Willy Gueret's net.
The Swans drew level nine minutes later as former Barnsley striker Rory Fallon executed a superb overhead kick with his left foot after Owain Tudur-Jones had nodded on a free-kick into the area.
Five minutes before the interval Swansea were gifted the lead as Tykes keeper Colgan allowed Andy Robinson 25-yard shot to slip from his grasp and trickle over the goal-line.
The second half started in a much more sedate fashion, before Barnsley made it 2-2 just past the hour mark. Brian Howard was hacked down just outside the area and Danny Nardiello curled his right-foot free-kick past the unsighted Guadaloupe-born Gueret.
Tykes skipper Paul Reid almost snatched a dramatic late winner as his header from Devaney's superb cross bounced up and over the crossbar, while Tate wasted a chance right at the death - slicing wide of the target from ten yards out.
Swans talisman Lee Trundle forced a fine save from Colgan early on in extra-time, but the City striker then wasted a clear chance when placing a close-range shot inches wide of Colgan's far-post midway through the second period of extra-time.
That left spot-kicks to decide the winners, with Barnsley scoring all four of their kicks, through Hayes, Chris Shuker, Paul Heckingbottom and Antony Kay to emerge as 4-3 victors.
Penalties
Lee Trundle scores for Swansea, 1-0 Swansea
Paul Hayes scores for Barnsley, 1-1
Leon Britton scores for Swansea, 2-1 Swansea
Chris Shuker scores for Barnsley, 2-2
Adebayo Akinfenwa misses over bar for Swansea, 2-2
Paul Heckingbottom scores for Barnsley, 3-2 Barnsley
Owain Tudur-Jones scores for Swansea, 3-3
Antony Kay scores for Barnsley, 4-3 Barnsley
Alan Tate has penalty saved for Swansea by Barnsley's Nick Colgan
Barnsley win 4-3 on penalties.
Swansea line-up :
Willy Gueret, Sam Ricketts, Gary Monk, Alan Tate, Kevin Austin, Leon Britton, Owain Tudur-Jones, Kristian O'Leary, Rory Fallon (Adebayo Akinfenwa 94), Leon Knight (Lee Trundle 69), Andy Robinson (Kevin McLeod 105).
Unused substitutes :
Brian Murphy and Tom Williams.
Barnsley line-up :
Nick Colgan, Paul Reid, Bobby Hassell, Paul Heckingbottom, Anthony Kay, Martin Devaney, Brian Howard (Dale Tonge 73), Stephen McPhail, Paul Hayes, Marc Richards (Tommy Wright 70), Daniel Nardiello (Chris Shuker 96).
Unused substitutes :
Scott Flinders and Neil Austin.
Referee - Lee Mason (Bolton).
Attendance - 55,419.
Shots on target - Swansea 10 Barnsley 5.
Shots off target - Swansea 16 Barnsley 3.
Hit woodwork - Swansea 0 Barnsley 0.
Offsides - Swansea 4 Barnsley 4.
Corners - Swansea 5 Barnsley 5.
Free-kicks conceded - Swansea 12 Barnsley 16.
Goals - Paul Hayes 19 (B), Rory Fallon 28 (S), Andy Robinson 40 (S) and Daniel Nardiello 62 (B).
Yellow cards - Brian Howard 44 (B), Bobby Hassell 45 (B) and Dale Tonge 109 (B).
Post-match quotes
Barnsley boss Andy Ritchie said after the thrilling encounter :
"The players were absolutely magnificent and they deserve a great deal of credit. And the crowd were also absolutely superb and the character of the players showed through. We always felt that we could get a goal back when we were 2-1 down and at half-time we got them to focus.
"We were under the cosh at the end and one or two of the players falling down with cramp and a few had injuries as well. They were a bit quiet at half-time which worried me a little bit but it's absolutely tremendous. I can't put it into words."
Tykes keeper Nick Colgan, who was at fault for the second Swansea goal, but turned from zero to hero after making the winning penalty save added :
"I wanted the roof to open up and take me up after my mistake. But that's the nature of goalkeeping, one minute you are the villain and the next you are a hero. If we'd lost 2-1 - no matter what has happened during the season - I would have been remembered for that reason."
Swansea manager Kenny Jackett bemoaned his players' finishing in front of goal, commenting :
"It's a bitter disappointment, particularly considering we had more chances and more of the play. I'm a little bit disappointed with the free-kick from which they scored. It looked like we offered the lad half the goal to sidefoot it into. But we had more than enough chances to win the game.
"The game was almost indicative of our season. But what we will do is come back even stronger. We'll make sure the disappointment we feel now will drive us on to be a more successful club next season."