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Doug Loft’s stunner counted for nothing as Gillingham let slip their one-goal lead.
Gills captain Loft struck from 30 yards to give his side a half-time lead at Boundary Park, but the advantage didn’t last as Timothee Dieng headed the hosts level in the second half and Jonathan Forte put them ahead.
It was the fourth time running that the Gills had failed to win on the road.
With Ryan Jackson still out injured, it meant a reshuffle, with Adam Chicksen starting right-back and Aaron Morris joining Max Ehmer in the middle.
Oldham began the match well and their recent signing, Curtis Main, stabbed a good chance wide after latching on to Daniel Lafferty’s ball forward.
But it was the Gills who took the lead through skipper Loft. He drilled the ball home from distance to put Edinburgh’s side ahead with his fourth goal of the season.
Oldham remained a threat but their finishing was poor.
Keeper Stuart Nelson made a block with his legs to deny Main, before seeing Aaron Amadi-Holloway and Forte send efforts wide of the mark.
The scores were level just before the hour mark when a Matthew Palmer floated the ball into the box and Dieng, unmarked, looped his header over Nelson.
There was another injury blow for the Gills midway through the half as Loft limped off, having taken a whack during a committed challenge that saw Oldham’s Matt Palmer booked.
Bradley Dack went close but had his effort turned over the bar by keeper Joel Coleman.
Oldham went ahead with 17 minutes left. Bradley Garmston’s weak clearance was picked up by James Wilson and his inviting cross was bundled home from close-range by Forte.
Edinburgh made a double substitution late in the game, handing George Williams his debut while Luke Norris joined Donnelly up front.
Oldham thought they had a third, after scoring from a corner, but Nelson was fouled in the process. Moments later the Gills keeper was called into action to save from Main.
The hosts kept the pressure on and it needed a good block from Morris to deny Anthony Gerrard, as Oldham took the points to boost their survival hopes.
Reaction: Justin Edinburgh "bitterly disappointed" with Gills defeat
Gillingham: Nelson, A Morris, Garmston, Ehmer, Loft (Hessenthaler 67mins), Wright, Chicksen, Osadebe (Norris 79mins), Dack, Samuel (Williams 79mins), Donnelly. Subs not used: G Morris, B Dickenson, M Dickenson, List.
Oldham: Coleman, Dieng, Wilson, Gerrard, Kelly, Lafferty, Dummigan (Winchester 75mins), Palmer, Forte, Amadi-Holloway (Murphy 79mins), Main. Subs not used: Cornell, Brown, Mills, Croft, Cassidy.
Attendance: 3,876 (279 away).