Latics secured their passage through to the second round of the Johnstone's Paint Trophy with a late strike from substitute Jordan Bove.
The youngster, who had only been on the field five minutes, finished past the goalkeeper to score his first professional goal for the club and win the game for Latics.
In an evenly contested first half, Latics had the first opportunity of the game on the tenth minute. Neat play in the midfield saw the ball fall to Brian Wilson on the right-hand side and his drilled cross almost caused an own goal but Jordan Pickford saved well.
Bradford responded and almost took the lead two minutes later. A cross from former Latics loanee Alan Sheehan found the head of Oliver McBurnie but the striker could not direct his header on target.
On his first start for the club, Amari Morgan-Smith was causing a nuisance in attack, winning headers and chasing the ball down with intent.
Midway through the half, Matty Dolan should have put the Bantams ahead but the midfielder mis-kicked his effort and the chance passed.
Both sides enjoyed good spells of possession but clear cut chances were proving hard to come by.
Latics almost took the lead just before the break through Morgan-Smith. Winchester's wonderfully picked out the striker in the centre but his header went inches wide.
Bradford started the second half brightly and should have taken the lead just before the hour mark.
Mark Yeates picked up the ball in the centre of the goal and struck the outside of the post with a fierce shot which went to safety.
Latics started to come back into the game and almost took the lead through a volley from Carl Winchester but the goalkeeper comfortably saved in the end.
The home side started to dictate the play and caused a succession of free kicks and corners but were unable to capitalise on them.
With both sides intent on not loosing possession, Latics finally made their pressure pay on 88 minutes as substitute Bove fired the winning goal.
The youngster pounced on a loose ball in the area after great work from Winchester to fire past the goalkeeper and score his first career professional goal.
Latics saw out the game and go into the hat for the next round of the competition.
Oldham Athletic: Rachubka, B.Wilson (Brown 89'), J.Wilson, Elokobi, Mills, Winchester, Jones, Kelly, Dayton (Bove 82'), Philliskirk, Morgan-Smith (Dieng 82').
Subs not used: Coleman, Tidser.
Bradford City: Pickford, Darby, Meredith (Clarke 74'), Dolan, Sheehan, McLean (Hanson 69'), Yeates, Kennedy, Routis, McBurnie (Bennett 69'), McArdle.
Subs not used: Knott, Williams.
Goals: Oldham Athletic (Bove 88') 1-0 Bradford City
Attendance:2,535 (660 visiting supporters)