The duo struck in the first half and Gills substitute Alan Pouton pounced for his second goal of the season on the stroke of full-time as the Dons were well beaten.
The first real opening came Gillingham's way on 18 minutes when Paul Shields flicked the ball to his strike partner Neil Harris in the box and his first-time 12-yard shot stung Matt Baker's fingertips.
Baker was then called in to action again, tipping an Andrew Crofts header over the bar, before Gillingham took a deserved lead on 26 minutes.
Michael Flynn delivered the ball to the back post, from a deep position on the right, Crofts headed back across goal and Johnson was on hand to head home.
On the half-hour mark Gills lost the lively Matt Jarvis through injury, but that didn't prevent them from doubling their advantage five minutes before the break.
Clohessy, still a member of Gillingham's youth team, moved forward from his right-back position to let fly with a low 25-yard strike in to the bottom corner.
MK Dons then nearly got back in to it on the stroke of half-time when Harris blocked Trent McClenahan's shot before clearing off the line.
In the second half Gillingham took their foot off the gas and allowed MK Dons a few sights of goal. Craig Morgan's diving header forced a superb save from Jason Brown, and then sub Stephen Quinn shot over from six yards when he should have done better.
Gillingham ended the year in style though when two of their substitutes - Gavin Grant and Pouton - combined to seal victory for Ronnie Jepson's improving side.