After a 30-minute delay due to a chip-shop fire outside the main stand, both teams ran on the pitch with very different looking sides that won on New Year's Day.
In a game which saw the home team dominate possession and chances, the outcome mirrored an FA Cup third round humbling by Shrewsbury Town in 2003 which David Moyes described as his worst defeat ever.
As expected, Everton started the brightest of the two teams and the home side kept the Latics camped in their own half for the first ten minutes.
The Toffees should have gone one up in the first 60 seconds after a neat through ball by James McFadden found striker James Vaughan one-on-one with keeper Mark Crossley, but the veteran shot-stopper was quickly off his line to deflect the ball wide.
The chances kept coming as Everton looked like they were playing more of a 4-2-4 formation with McFadden and Steven Pienaar bombing forward on both wings.
Oldham took a while to settle but their first chance came from a high looping cross which had keeper Stefan Wessels flapping, but Craig Davies could only swing and miss to leave an easy clearance for Lee Carsley.
The home side looked to be turning the screw once more as a shot was cleared off the line with only minutes to go before half-time, but the visitors conjured a piece of magic sent the 5,500 travellers crazy.
A pass from star man Kelvin Lomax found Gary McDonald in the middle of the pitch and he unleashed a left-footed screamer from 25 yards that looped over a stranded Wessels to give Oldham a 1-0 lead at half time.
Off the back of six straight away wins, the visitors were full of confidence and came out for the second half in total contrast to the first with the whole team fully charged from the late goal.
The Toffees felt a bit hard done by on 55 minutes after a penalty appeal for handball was waved away by referee Uriah Rennie after a strike in the box by Carsley looked to hit a flailing orange arm.
With 25 minutes to go, Moyes brought on strikers Ayegbeni Yakubu and Victor Anichebe and the home side started to turn up the pressure in search of the important equiliser.
The Toffees should have pulled level moving into the final 15 minutes but a weak side-footed effort from Yakubu was almost met by fellow substitute Anichebe seven yards out, but the spin on the ball took it away from the striker's boot.
Chance after chance went begging for the home side as McFadden and Joleon Lescott came close with headers, but with time running out each wave of attack looked fruitless as the Oldham defence stood strong.
With almost the last kick of the game, an Anichebe cross found the head of McFadden whose nod-down fell at the feet of top-scorer Yakubu, but the striker could only hit the post with a left-footed effort.