Poland under-21 international Abbott lobbed keeper Les Pogliacomi from the edge of the box on four minutes after defender Will Haining scuffed an attempted clearance.
The early goal forced caretaker boss Tony Philliskirk to ditch Oldham's 4-1-4-1 formation in favour of a more conventional 4-4-2 line-up.
But it did not prevent the Latics from conceding their 18th goal in the last five outings. Haining was again at fault when he failed to clear Delroy Facey's cross on 29 minutes to gift Abbott a close range tap-in.
Abbott has now scored 21 goals this season and he nearly turned provider a few minutes later when he played Chris Brandon in down the middle, but Pogliacomi parried his effort.
And Facey, making his debut on loan from Hull after signing on Saturday morning, should have added another when he intercepted Oldham defender Danny Hall's weak back pass.
Facey romped goalwards and tried to lift the ball over Pogliacomi, but the keeper made a fine save to keep the score down.
Oldham's defending throughout the first half was poor and it was easy to see why they have conceded five against Bristol City and Wrexham and four against Bournemouth in recent games.
Philliskirk tried to remedy the problem by bringing on Guy Branston and David Eyres for Hall and Adam Griffin in the second half and it paid dividends.
The visitors went on to dominate the rest of the encounter and should have at least ended up with a draw.
Mark Hughes had a goal ruled out for offside before Branston netted from Matty Appleby's free-kick on 75 minutes.
And in the closing stages Chris Killen blasted over the bar after being put clear by Kevin Betsy's through ball.