The first league meeting in nearly 30 years between these sides looked to be heading for a stalemate until the Addicks took the lead on 79 minutes thanks to a disastrous own-goal from Gills left-back John Nutter.
But Simeon Jackson was once again the hero for the Gills as he slotted home his 11th goal of the season just four minutes later.
He said: "It was a very tough game and when it's like that you have to roll your sleeves up and stand up to be counted. I thought we did that well today and despite there not being a great deal of quality from us we were able to grind out a result.
"It was a cup-tie tempo out there and we showed great strength and character to get a result out of the game.
"The target for us is promotion and results like this are important to keep things ticking over and the points coming. A point was a fair result and I think their goalkeeper Rob Elliot was the difference - he pulled off some unbelievable saves."