Dan Nlundulu opened his Cheltenham scoring account, tapping home a saved Callum Wright effort to bag the only goal of the game.
Cheltenham will feel they could've added to their tally, with two chances falling to Wright midway through the first half.
With only ripples coming from the Charlton attack throughout the second half, it was a last-minute corner brushed in by second-time debutant Chuks Aneke that equalised.
Story of the match
The Addicks racked up the corners in the early stages of the game, as they tried to make their aerial presence count, piling pressure on Owen Evans' goal.
However, it was the Robins who ended up with the clearest of opportunities early on, as striker Alfie May found himself through on goal.
The tightest of angles for May was closed down even further by goalkeeper Stephen Henderson.
Cheltenham continued to pile on the pressure, as Leicester City loanee Wright was slipped in, and in an attempt to chip the keeper, found his shot saved by Henderson.
New signing Nlundulu looked fired up and proved to be a handful for the Charlton defence, with his physical presence helping Duff's side advance through the thirds.
Wright again found himself with a golden opportunity, as Sean Long drove a cross over the goal-line, with the 21-year-old unable to tap the ball home into an empty net.
Wright twisted and turned on the edge of the Charlton box, firing a low driven shot towards the goal, which was parried away by the ‘keeper.
The save fell only as far as Nlundulu who was on hand to score his first Cheltenham goal in only his second appearance for the club.
Matty Blair had the opportunity to double their advantage shortly after, his chop inside the defender carving out a 1-on-1 chance, a low shot yet again saved by Henderson.
Boss Jackson looked for a second-half reaction as he brought on Corey Blackett-Taylor in place of Diallang Jaiyesimi.
And it was Charlton who came racing out of the blocks in the second half, as debutant Aneke attempted an acrobatic effort, only for it to hit the top of the crossbar.
In end-to-end fashion, May then found himself unmarked at the back post, striking a volley that had to be cleared off the line by the Addicks defence.
Former West Ham United man Elliot Lee then lofted a volley towards the Robins goal, forcing the first big save of the game from glovesman Evans.
A diagonal ball from Wright allowed May to once again, gain some space, his back-spinning volley placed just wide of the left-hand post.
Defender Matty Pollock then headed wide from point-blank range, with the on-loan Watford man in acres of space in the Addicks box.
As the game petered out, Charlton threw men forward for a corner which was diverted towards goal by Ryan Inniss, with Aneke getting a toe on the ball to tap past Evans - a late blow for the Robins.
Man of the match - Dan Nlundulu
The Southampton loanee proved to be a nuisance for the Charlton defence all afternoon.
Although it'll be his goal that's sure to grab the headline, his ball-carrying ability meant Duff's side could move up the pitch effectively.
His poacher's instinct also meant he bagged the first strike of the clash, a simple case of right place right time for him.