كتب : Omar AbdelAziz
A ninth minute strike from midfielder Joe Ledley was enough for the Welsh club to end Barnsley's heroics in the competition.
Cardiff, who are currently 12th in the English Championship, have last-time reached the FA Cup final in 1927, when they won the trophy.
The Bluebirds will face Premiership side Portsmouth on May 17th at Wembley, after Pompey beat West Brom 1-0 on Saturday.