The Tykes looked to be in control thanks to a goal in each half from Chris O'Grady at Oakwell, but Chris Powell's men fought back toleave both sides on one point.
The collapse will be sure to cause Tykes boss Dave Flitcroft some frustration, but he can at least console himself with the knowledge that his side do have goals in them after three blank appearances in all competitions so far this term.
With dissent already showing after a poor start to their season, Barnsley were desperate to set an early tempo and that they did, opening the scoring with 16 minutes gone.
Scott Golbourne picked out Chris Dagnall with a cross and, even though he was shut down, O'Grady was alert to ram in the loose ball.
Charlton's response consisted of a Callum Harriott effort which Luke Steele tipped away as the home side remained in control.
The second goal they were chasing duly followed too, as O'Grady leapt to get on the end of Mellis' 55th-minute cross and beat Hamer with a neat header.
It was a far cry from Charlton's 6-0 win on the same ground a matter of months ago, but they quickly set about getting themselves back into things.
Cousins was the first to contribute with 26 minutes left, picking up a half-cleared ball in the Barnsley area and slotting in.
It put Barnsley on the back foot and with their early intent lost, Church punished them just eight minutes later.
The Wales international chased down Yann Kermorgant's lofted pass and managed to put enough on his shot to beat Steele and the recovering Tom Kennedy.
That set up a tense finish but both sides seemed happy to hold what they had as they picked up their respective first points of the season, with only Leon Cort looking dangerous with a free header which went wide.