Both sides went into the game on the back of poor recent results but Ronnie Moore's team surprised the hosts with a goal in only the third minute of the match.
Captain Andy Liddell swung in a free-kick that eluded everyone except Kiwi international Chris Killen and he stooped to head past Jason Brown from close range.
Neale Cooper's side tried to get themselves back in the game immediately but found the Oldham defence a tough nut to crack with Terrell Forbes looking particularly impressive.
Liddell almost doubled Oldham's lead on the half-hour mark when his curling free-kick was brilliantly saved by Brown.
But despite their pressure Gillingham could only force a series of corners and Darren Byfield had two appeals for a penalty turned down by referee Russell.
Gillingham came out for the second period a different team and could have equalised just three minutes in when Matthew Jarvis' curling shot went just over.
They continued to press and had more decent penalty shouts turned down before Ian Cox's glancing header from a corner bounced on to Chris Day's far post and away to safety on 63 minutes.
Oldham relied on the long ball to relieve the pressure on their defence but they were mostly penned back inside their own half as Gillingham maintained their fast attacking pace.
Two golden opportunities fell to the home side in the last five minutes but first substitute Paul Shields could not beat Day with a close-range volley before Jarvis' stinging shot was well saved by the Oldham keeper.
Substitute Steve Hislop almost equalised in injury time but his header agonisingly looped on to the crossbar.