Paul Dickov's side had to wait 77 minutes for the breakthrough, but their patience was rewarded by goals from Matt Derbyshire and Jose Baxter.
Oldham almost went in front after eight minutes as Baxter's 16-yard shot brought a save from visiting keeper Ryan Allsop. Baxter also headed over before Oldham keeper Dean Bouzanis did well to save a dipping Martin Rowlands volley.
Lee Croft drilled wide for the home side, while Jean Yves Mvoto wasted two headed chances. Orient could have cashed in through Moses Odubajo, who touched wide at full stretch, before Allsop denied Oldham captain James Wesolowski.
Oldham grabbed their opener when Croft's corner was helped on to Derbyshire for a simple two-yard finish.
Six minutes later, Baxter doubled the lead by turning on the edge of the box and curling home an excellent shot.