Captain Izzy Whittle's brace appeared to have earned Belles the bragging rights at Rossington Main.
But Sophie Bell equalised in stoppage time and Mollie Crump scored late in extra time to send the Reds through to the next round.Â
Amy Woodruff gave Barnsley the lead midway through the first half.
Doncaster had come from behind when Whittle headed them level on 70 minutes but the best of the topsy turvy actionÂ was still to come.
It had appeared as though the Belles had won the game when Whittle headed them in front two minutes from time.
But the Reds produced the first instalment of their late heroics when Bell netted in injuryÂ time to take the game into extra time.
A scrappy finish from Crump two minutes from the end of extra time earned Barnsley's passage in the competition for teams knocked out of the FAWNL Cup.
Belles host Shaw Lane Aquaforce LadiesÂ in the County Cup on Sunday.