The Addicks took the lead on 79 minutes thanks to a disastrous own-goal from Gills centre-half John Nutter before Jackson slotted home his 11th goal of the season just four minutes later.
The action began in the first minute when the lively Izale McLeod went down in the Gills box but his early penalty appeals were waved away by referee Jon Moss.
In the 24th minute McLeod should have scored after turning John Nutter on the edge of the box but fired high and wide with his left-foot.
No goals looked forthcoming until the 79th minute when Nutter sliced a right-foot clearance from an innocuous Therry Racon cross into the bottom corner of his own net giving Simon Royce no chance.
But Jackson equalised three minutes later with a good finish from six yards out after a Mark Bentley flick-on to level the scores and that is how it stayed.