Richard Butcher and Luke Beckett both scored in the first 12 minutes and Bradford were unable to fight back for a point despite a 12th goal of the season from veteran Dean Windass.
Bradford found home goalkeeper Chris Day in defiant form and also missed several chances to end their worrying slide.
Oldham appear to be heading in the other direction as they have gone six games without defeat in League One.
The Latics went ahead on just seven minutes when defender Danny Hall crossed from the right to Beckett. The striker found Butcher 18 yards out and he stroked the ball into the bottom corner for his first goal of the season.
Tempers soon flared and Danny Cadamarteri was booked for a wild tackle on Richie Wellens and both Wellens and Paul Warne were booked for retaliation in the next two minutes.
But Oldham doubled their lead with a flowing move which ended when Butcher had his shot blocked and Beckett followed up to convert the rebound from eight yards.
Oldham's Mark Hughes shot just wide from long range as the home team stayed firmly in control of the Roses battle.
But Bradford got themselves back into it in first-half stoppage time after defender Guy Branston was adjudged to have fouled David Wetherall from a corner.
The referee gave a penalty which Windass slotted into the bottom right-hand corner, just beating Day's effort to save.
It signalled an improvement from the visitors who went close after 54 minutes through Ben Muirhead.
Substitute Andy Cooke fired at the keeper just after replacing Bobby Petta and Windass was guilty of a bad miss as Oldham buckled.
Donovan Ricketts made a good low save from Beckett to keep his side in the running and they were denied again on 89 minutes when Day saved from Steve Claridge.