The two teams are now level on points after this hard fought contest at The Valley with Charlton keeping their first clean sheet in nine games to seal victory.
The goal in the 83rd minute was a header from winger Lloyd Sam, but the home side were indebted to their goalkeeper Nicky Weaver who made a brilliant reaction save with his legs in injury time to deny Stoke substitute Jon Parkin an equaliser.
Charlton had the better of the exchanges, but Stoke showed why they had only been beaten twice in 14 matches on their travels with some excellent defending and they always looked dangerous on the counter-attack.
The home side had a couple of efforts blocked in the first half of very few chances, but it was Stoke who should have taken the lead 30 seconds into the second half when Ricardo Fuller saw his shot, which was goalbound, turned away by Weaver.
Stoke keeper Steve Simonsen made a fine save to deny Darren Ambrose but it was Charlton substitute Luke Varney who set up the winner.
He had a great chance to score himself but made a mess of his shot.
He managed to regain control of the ball and crossed for Sam to make the finish and send the home fans home very happy.
Charlton's new £1.5million striker Andy Gray from Burnley failed to get on the scoresheet, but his link-up play proved important for the home side.
After they fell behind, Stoke lost their heads a little and gave away a series of fouls which did not help their cause.