The winger, a summer signing from Cardiff, picked the perfect moment to bag his first goal for the club, and it could have been even better for the home side as Marlon King saw his late shot rebound off the inside of a post.
But Blues' strong finish masked what was a sloppy performance littered with misplaced passes and a lack of creativity, which only gained much-needed inspiration following the second-half introduction of Nikola Zigic.
Jacob Butterfield's clinical long-range strike looked to have ended Birmingham's 100% home record in the npower Championship with defeat.
It was the first league goal Blues have conceded on home soil this term and Danny Drinkwater went close to a second when his effort from distance clipped the crossbar.
Nevertheless, the draw extends the Yorkshire side's unbeaten sequence to five matches while also ending a run of three successive defeats for City.
Birmingham's line-up showed six changes from the heavily rotated XI who relinquished the club's hold on the Carling Cup with a 2-0 defeat at free-spending Manchester City in midweek.
And manager Chris Hughton was forced into a defensive reshuffle after just nine minutes as centre-back Curtis Davies was stretchered off down the tunnel with a serious-looking knee injury.
But that was not Hughton's only problem as Blues struggled to get going.
Jim O'Brien fired a half-chance over the crossbar for Barnsley before Drinkwater sent a free-kick harmlessly over from distance.
Birmingham were posing next to nothing of an attacking threat in what was proving to be a lacklustre encounter, with Tykes midfielder Matty Done forcing a comfortable save from Boaz Myhill after 25 minutes with what was the game's first shot on target.
Done - making his return from injury - was then forced off shortly after but the visitors remained the most likely to break the deadlock, Myhill turning Butterfield's effort around a post.
And it was no surprise when Barnsley broke the deadlock, skipper Butterfield this time beating Myhill as he sent a superb strike into the bottom corner from around 30 yards.
The goal raised the hosts somewhat and Ridgewell headed over crossbar from Jean Beausejour's corner before Chris Wood fired wide but, as the half-time whistle was greeted by a chorus of boos from the home support, Blues were yet to register a shot on target.
The home side showed little sign of improvement after the restart and Hughton sent on Wade Elliott and Zigic in an attempt to change things.
And the latter, making his first league appearance since early April due to injury, added much-needed impetus for Birmingham.
Zigic's presence caused panic in the Barnsley area after 69 minutes and led to City's first goalbound attempt - King heading at Luke Steele.
Elliott then saw his shot bravely deflected off target by Jim McNulty.
At the other end, Drinkwater's long-range effort struck the top of the crossbar before Blues' late rally.
Burke curled into the bottom corner from 25 yards with four minute remaining before King could only watch as his right-footed effort hit the inside of a post and went away to safety, much to the relief of Barnsley.