Gillingham opened brightest on a bitter evening at Edgeley Park.
Barcham tested home keeper Owain Fon Williams, then Simeon Jackson twice blasted well wide from good positions.
However, it was to be the hosts who went in front on 17 minutes.
Craig Davies fed Stephen Gleeson on the left and the young Irish midfielder fired home from 15 yards after beating keeper Simon Royce at his near post.
It only took Gillingham seven minutes to get back on terms though.
Jackson played a neat ball to Barcham and he lashed home a crisp, angled drive to make it 1-1.
Just past the half-hour mark, the League Two side roared into the lead thanks to another decent finish.
This time Adam Miller superbly played in Barcham and he coolly slotted home his second goal of the night.
A bad night for Stockport got worse just before the interval as skipper Michael Raynes limped off to be replaced by Northern Ireland international striker Peter Thompson.
Gillingham had the first chance of the second-half. Curtis Weston played in Jackson but he smashed over from just inside the box.
Weston was then denied by his own player Jackson, who somehow managed to divert a goal-bound effort wide of the target.
Johnny Mullins headed over for the hosts and Tommy Rowe was denied by Royce, but it was to be Gillingham's night.