The Latics began Tuesday's contest one place and two points behind Simon Weaver's men in the League Two standings, while also boasting the division's worst defensive record.
But, they left North Yorkshire with a clean-sheet and a richly-deserved victory courtesy of some bright attacking play that was aided by some poor Harrogate defending.
In truth, their margin of victory could have been far greater, though things might have unfolded rather differently had the hosts capitalised on a good opportunity to take the lead within a few seconds of kick-off.
Cameron Borthwick-Jackson's error allowed Jon Stead the opportunity to pull the ball back from the right edge of the penalty area, though Josh McPake's far-post finish was blocked superbly by the sliding Harry Clarke.
At the other end, Borthwick-Jackson forced a save from Joe Cracknell with a header at a left-wing corner before Oldham took the lead following another set-piece from the same side.
The initial delivery was cleared to the edge of the box, but met by Alfie McCalmont who smashed home a sweetly-struck effort via the underside of the cross-bar.
The 25 minutes that followed belonged to the home side, with the Latics barely getting a kick of the ball.
But despite spending an extended period stuck in their own territory, Athletic survived and went on to finish the half very much in the ascendancy.
Borthwick-Jackson should have made it 2-0 on 38 minutes, but his free header from another dangerous right-wing corner was somehow kept out at point-blank range by Cracknell.
A poor clearance by Cracknell was then met by a loose touch from Lloyd Kerry in the centre circle as he tried to retrieve the situation. This allowed McCalmont to slip the ball into the path of Dylan Bahamboula, though the big centre-forward could only pick out the side-netting.
Oldham kept coming and Conor McAleny's stinging strike drew another decent stop out of Cracknell shortly before a half-time whistle which came at a good time for the home side.
The interval should have provided Harrogate with the opportunity to re-group, but for the fourth time in five matches they made a dreadful start to the second period and conceded within a minute of the resumption.
Left-back Mitch Roberts was caught out of position as Clarke raided at serious pace down the Latics' right and drew a parry out of Cracknell. Bahamboula was however on hand to pounce on the rebound, taking a calm first touch before firing into the gaping goal.
Conceding for the second time visibly knocked the stuffing out of Town, though Glasgow Rangers loanee McPake did his best to try and get them back into the contest with some driving runs down the left.
But, one George Thomson free-kick aside, visiting goalkeeper Laurie Walker was hardly troubled and the third goal of the night arrived at the opposite end of the field.
Cracknell took far too long clearing his lines, Athletic substitute Blackwood charged down his kick and the ball rolled into an empty net to round of a night to forget for Weaver and his men.
Substitute Ryan Fallowfield came as close as anyone in yellow and black to netting a consolation with a low blast which Walker did well to push away, though Marcus Barnes squandered a glorious chance to make it 4-0 when he stabbed wide of the mark with just Cracknell to beat.
And the same player went one-on-one with the Sulphurites stopper once again in stoppage-time, but was again unable to find a finish as Cracknell got down well to smother the ball.
Defeat sees Harrogate drop one place to 17th in the table.
Harrogate Town: Cracknell; Burrell (Fallowfield 79), Smith, Hall, Roberts; Thomson (Kiernan 83), Falkingham (Williams 83), Kerry (Francis 79), McPake; Muldoon, Stead (Beck 75). Unused substitutes: Belshaw.
Oldham Athletic: Walker; Jameson, Piergianni, Borthwick-Jackson: Clarke, McCalmont (Garrity 71), Whelan, Adams (Badan 82); Bahamboula (Barnes 65), Keillor-Dunn (Vaughan 82), McAleny (Blackwood 72). Unused substitutes: Bilboe, Fage.
Referee: C Boyeson (East Yorkshire).