The Welsh side looked to have earned a priceless point to keep up the heat on the leading pack until the late heart-breaker.
Mark Hudson handled just outside the area to give the home side a free-kick and Dickinson, on loan from Stoke City, stepped up and smashed in a low shot that deflected in off the wall.
Early on City's Chris Burke impressed down the right but saw his shot well saved by Luke Steele after he had rounded Dickinson.
And when Joe Ledley curled in a testing corner he beat Steele but Rob Kozluk headed off the line to deny the visitors.
At the other end Dickinson's super curling cross needed only a touch from Daniel Bogdanovic or Jon Macken but they were inches away and Ryan Shotton's header from Kozluk's free-kick was well held by David Marshall.
Another Dickinson cross from the left found Bogdanovic but his header was straight at the keeper.
Barnsley caught out the Welsh side when Franca Anderson Silva's superb cross-field pass triggered a powerful run by Bogdanovic but, as the Malta international had the goal in his sights, Burke raced back to get in a last-ditch challenge.
After a half-time rocket from manager Dave Jones, Cardiff found a new lease of of life after the break and almost edged in front.
Peter Whittingham's accurate cross was met by Burke but his close-range header hit Dickinson when he looked certain to score.
But Barnsley had a chance of a breakthrough when Adam Hammill's free-kick found Ryan Shotton but the header was high.
Barnsley midfielder Hugo Colace pounced on a loose ball after 63 minutes and smashed a fierce low shot but a deflection carried it wide.
Tykes striker Iain Hume came off the bench after 69 minutes and immediately caused headaches for the visitors with tricky footwork just outside the area.
The Canada international won a free-kick and took it himself but his low shot was just wide of the target.
And Colace came close to a late winner after great work by Hammill but he volleyed over before Dickinson had the last word.