The centre-back nodded the visitors in front amid pouring rain in the 35th minute, only for Jonathan Greening to equalise almost immediately from long range with his first goal since joining on loan from Nottingham Forest last month.
Barnsley were the better side and missed plenty of chances against a Blues outfit who were disorganised defensively, with Craig Davies, a boyhood Blues fan who scored four goals in September's 5-0 rout at St Andrew's, blazing over a second-half penalty after Steven Caldwell's handball.
And the hosts were punished almost immediately as Curtis Davies, unmarked from another set-piece, converted his fourth header in six games to clinch matters in the 77th minute.
Barnsley enjoyed the better of proceedings early on, Jim O'Brien seeing an effort blocked by Curtis Davies although the visitors did force a succession of three corners in which they failed to prosper.
Luke Steele was still to be called upon as the half-hour mark passed, with Barnsley much the stronger.
But, out of nowhere, Curtis Davies headed Birmingham in front. Robert Hall delivered another excellent set-piece, Birmingham's main threat, which Davies nodded home unchallenged at the near post.
However, the lead did not last long as Birmingham's frailties in defence were fully exposed. Barnsley applied pressure almost straight from kick-off with Dawson seeing a strike blocked and, with the visitors struggling to fully clear their lines, the ball broke for Greening, who converted low from distance.
The visitors' defence was exposed again within a minute of the restart but a swift move ended when Chris Dagnall could only slide the ball behind.
John Stones saw an effort blocked by a late Blues tackle and, with the game flowing from end to end, Barnsley were awarded a spot-kick in the 73rd minute for a somewhat harsh handball decision against Caldwell. But Craig Davies, who had only been on the pitch five minutes, blazed his spot-kick high over the bar.
A superb stop from Jack Butland kept out a header from fellow sub Matty Done before Curtis Davies then settled matters in the 77th minute via another inch-perfect delivery from Hall.