Athletic dominated large parts of the game but were undone in the final minute as Josh Law poked through his own goal to cap off a cruel afternoon for Latics.
Manager Stephen Robinson made one change to his starting 11 from last weekend as Cameron Burgess replaced the injured Charles Dunne at central defence.
It was a positive start from Oldham Athletic as Darius Osei almost nicked the ball off the last defender Nathan Pond but the defender just recovered.
Worrying signs followed as Peter Clarke was clattered from a corner into the box but after treatment the defender was fine to continue.
He would get straight back into the action as he blocked a goal bound Jack Sowerby effort from the edge of the box.
Latics had a half chance on the 13th minute as good work from Paul Green saw him cross to striker Billy Mckay but he could not direct his header on target.
It was a midfield battle mainly with both sides cancelling each other out.
Ashley Hunter almost forced a breakthrough midway through the half as his neat one-two with Bobby Grant saw his effort blocked by Clarke.
However, Latics did look the more threatening in attack. Ryan Flynn won the ball well, fed Osei who took the ball beyond his man, he crossed into the centre but Mckay’s shot was saved by Alex Cairns in the Fleetwood Town goal.
David Ball struck over Connor Ripley’s crossbar just after the half hour mark whilst Latics took the game to the Cod Army in the final 10 minutes of the first half.
Flynn cut inside his defender and unleashed a fierce effort which went past the post whilst on the left, Ryan McLaughlin’s pace was causing problems for the Fleetwood defence.
He won a free kick five minutes before the break but Josh Law’s clipped free kick could not find the head of a Latics man.
Athletic continued until the end of the half and McLaughlin forced a good save from Cairns but it would end goalless at the break.
Robinson’s men continued to attack in the second half and went close on 50 minutes on two occasions.
Firstly the ball sat up perfectly for Cameron Dummigan to strike on the volley but his effort was blocked for a corner.
From the resulting set piece, Law fed Clarke on the edge of the box but the defender’s shot was saved by the goalkeeper.
The visitors did start to come back into the game and that was soon after the introduction of Devante Cole.
Ashley Hunter curled goalwards from 25 yards which had Ripley scrambling but it went past the far post before Cole had a golden opportunity two minutes later.
The striker received the ball in space, behind the defence but Brian Wilson just did enough to put the striker off in front of goal as he skied from six yards.
Latics themselves had a massive chance to take the lead on 69 minutes as Osei raced beyond the last man, only had the goalkeeper to beat but Cian Bolger managed to get back and tackle the striker.
Robinson brought Lee Croft, Freddie Ladapo and Ollie Banks into the action and the changes worked well for Latics.
Heading into the final 10 minutes of the game, it was Latics who was taking the game to the hosts with Croft influential going forward.
Ladapo found space on 85 minutes but his shot was deflected away from danger, before Fleetwood started to fight back into the game.
Fleetwood Town substitute Chris Long weaved his way into the penalty box two minutes from time but Ripley pulled off a tremendous save to deny the striker.
As the fourth official advertised four minutes of additional time, Fleetwood Town took the lead through a fortuitous own goal.
A teasing cross was delivered into the box and Law got a toe to the ball at the front post and it trickled over the line to win Fleetwood Town the game.
They did have the ball in the back of the net again minutes later but Long was adjudged to be offside as he placed the ball beyond Ripley.
For all Latics dominance, they could not get the goal and were punished in the final minute.
Fleetwood Town: Cairnes, McLaughlin, Bell, Pond, Ball, Grant, Bolger, Glendon, Hunter (Long 76’), Sowerby (Nirennold 71’), Dempsey (Cole 55’).
Subs not used: Neal, Davis, Haughton, Roberts.
Oldham Athletic: Ripley, Wilson, Clarke, Burgess, Dummigan, Law, McLaughlin, Green (Croft 64’), Flynn (Banks 76’), Mckay, Osei (Ladapo 71’).
Subs not used: Kettings, Edmundson, Fane, Winchester.
Goals: Fleetwood Town 1-0 Oldham Athletic