The Kent side went in front through Dennis Oli, but they had no answer to a battling comeback by Oldham who could have won by a much bigger margin.
Gillingham have won just once in 2008 and their away form is a major concern as they have taken only eight points this season from a possible 45.
Boss Mark Stimson admitted they were in trouble, saying: "I have not mentioned relegation until now but we are in a sticky position and we need to do something."
Oldham made the better start and Chris Taylor tested keeper Simon Royce with a powerful shot in the third minute.
But Gillingham took the lead on 25 minutes as Nicky Southall sent over a cross from the right and Oli touched home from four yards after keeper Mark Crossley was unable to gather.
Oldham struggled to create chances but drew level shortly before half-time when young striker Lewis Alessandra played in Taylor, who reached the ball just before Royce and slipped in his second goal of the season from 12 yards.
There was only one team in it after half-time and Gary McDonald shot just wide before Alessandra was unlucky with a volley on the turn.
Oldham's winner came after 67 minutes when McDonald set up Craig Davies, who took a touch before smashing in from just inside the box to take his tally to 12 goals for the campaign.
Davies wasted a clear chance to increase Oldham's lead before McDonald hit the bar with a piledriver from 25 yards in injury time.
Gillingham were lucky to escape a humiliating defeat, but Oldham's season is on the up and they have not given up hope of a late run towards the play-off places.