Nick Proschwitz, making his debut after signing on loan from Hull, gave Barnsley the lead before goals from Tom Cairney and Rudy Gestede put the visitors in the driving seat at half-time.
In the opening few minutes, Cairney tried a shot from long range which was turned wide by Luke Steele.
The Barnsley goalkeeper was called into action again shortly afterwards, blocking a Gestede shot with his legs.
As the visitors continued to pose an attacking threat, David Dunn tried a chip but the ball drifted wide of the target.
Blackburn's Tommy Spurr then saw his deflected shot easily gathered by Steele.
Proschwitz had Barnsley's first chance of the match but he shot straight at Paul Robinson after finding himself one-on-one with the keeper inside the area.
Steele again came to Barnsley's rescue, parrying a shot from Jordan Rhodes, before the home side took the lead after 29 minutes.
Proschwitz got on the end of a ball played in from the right by Dale Jennings and fired past Robinson.
Blackburn threatened to respond almost immediately when Gestede had a chance with a header but he put the ball over the bar.
After a little bit of trickery, Jennings then put a rising shot over.
However, Cairney equalised in the 37th minute with a superb 25-yard effort, beating Steele when there appeared to be nothing on.
Just a minute before the break, Gestede then put the visitors in front, with Dunn taking much of the credit for the goal.
Dunn produced a surging run into the area before slipping the ball to Gestede on his right, who calmly slotted it past Steele.
Barnsley introduced Paul Digby at the resumption of play, with the youngster taking over from Stephen Dawson in midfield.
The hosts made a good start to the second half with Jim O'Brien putting a low drive wide.
Brek Shea's tenacity just outside the area then set up a chance for Proschwitz, who fired in a low shot which forced Robinson to get down smartly to his right to parry.
Barnsley manager Danny Wilson had used all three substitutes by the 61st minute, with Tomasz Cywka and Liam Lawrence also joining the action.
And it was Lawrence who had a hand in Barnsley's 69th-minute equaliser.
Referee Sebastian Stockbridge awarded a penalty after Lawrence was bundled over by Grant Hanley and O'Grady sent Robinson the wrong way from the spot.
Blackburn suffered a further blow a few minutes later when Lee Williamson suffered an injury which resulted in him receiving lengthy treatment before he was carried off on a stretcher.