Parkin had only been on the pitch for five minutes after replacing Ricardo Fuller when he collected a pass from Mamady Sidibe 12 yards from goal.
The big striker turned past his marker and slotted a well-placed shot beyond Nicky Weaver.
Stoke had set off at a frenetic pace, forcing six corners in the first eight minutes and putting the visitors goal under severe pressure.
Richard Cresswell made a bright start to his own debut, bringing a fine save from Weaver and causing all sorts of problems for Yassin Moutaouakil.
And Stoke should have taken a 15 minute lead when Fuller and Sidibe combined to set up Rory Delap, who shot wide with the goal at his mercy.
Charlton almost made Stoke pay with their first sign of class four minutes later as Darren Ambrose shot narrowly wide from Jose Semedo's perfect pass.
Stoke suffered a blow in the 33rd minute when injury-prone right back Stephen Wright, on loan from Sunderland, was stretchered off and replaced by Lewis Buxton.
But City continued to dominate and Dominic Matteo headed wide when it looked easier to score from Liam Lawrence's 42nd minute corner.
And Sidibe was guilty of an even more spectacular miss just before half-time when he miscued after a header from Ryan Shawcross was blocked into his path.
It was no surprise when an unhappy Alan Pardew made a double substitution at half time, bringing on Jerome Thomas and former Stoke favourite Chris Iwelumo.
And Charlton took a 55th minute lead after sloppy play by Delap led to Shawcross fouling Reid on the edge of the box.
Reid smashed a free-kick and his powerful shot took a deflection to leave Steve Simonsen helpless.
But Stoke drew level less than two minutes later when Fuller spun past Madjid Bougherra and clattered an unstoppable 20-yard shot beyond Weaver.
The high tempo of the game continued, but there were few chances before Parkin struck the decider.