Peter Clarke put Latics ahead in the opening five minutes of the game, powering home at the back post.
However, Bradford equalised through a controversial penalty decision as Ousmane Fane was adjudged to have fouled Billy Clarke in the penalty area.
He picked himself up to convert the penalty and equalise for the Bantams.
The result means Latics extend their unbeaten league run to four games and they are still yet to concede a goal from open play in the league.
Manager Stephen Robinson reverted to the same side which beat Bury last weekend with Ryan Flynn, Paul Green and Billy Mckay restored to the starting 11.
In what was a pulsating first half, Latics started well and took the lead early on through captain Peter Clarke.
The central defender rose highest from Marc Klok’s free kick into the box and powered home at the back post to give Latics the perfect start.
Robinson’s men did want to settle for one goal and went in search of another. Ryan Flynn weaved his way into the penalty, similar to his goal against Wigan Athletic and forced a smart save from Colin Doyle.
However, despite Latics’ goal advantage, Bradford piled on the pressure and had opportunities to equalise.
After Tim Dieng’s shot from the edge of the box was deflected wide, from the following corner Connor Ripley pulled off a wonder save to deny Mark Marshall from the edge of the box.
The goalkeeper’s one handed heroics set the tone of the rest of the half as Latics defended superbly throughout.
Latics should have been awarded a penalty on 13 minutes after Billy Mckay was fouled in the penalty area but the referee shook his head.
The home side continued to come forward and West Ham loanee Josh Cullen should have equalised on 20 minutes.
He won the ball in midfield, raced at the defence but dragged his shot wide of Ripley’s goal after going one-on-one with the goalkeeper.
Bradford’s pressure forced Robinson to change tactics and Latics set up in a 4-1-4-1 formation when not in possession.
That move stemmed the pressure and Latics had a great chance to extend the lead on the half hour mark.
Lee Erwin found Josh Law on the overlap and he crossed into the centre for Billy Mckay but his header fell wide of the post.
Law received the first booking of the half on 35 minutes after a late tackle as both sides finally started to settle into the game.
However, going into first half stoppage time, Latics again had to withstand some heavy pressure.
The best chance of that period came deep into added on time as James Meredith’s teasing cross found the onrushing Billy Clarke but he fired inches wide of Ripley’s goal.
Klok was booked five minutes into the second half for what the referee perceived as time wasting, but the midfielder claimed he did not hear the whistle.
Ripley was again forced to make a good save minutes later as Jordy Hiwula volleyed goalwards but the goalkeeper beat his fierce effort away.
However, seconds later, Bradford were awarded a penalty for a soft challenge in the penalty area which enraged the Oldham Athletic supporters behind the goal.
Ousmane Fane was adjudged to have brought down Clarke in the penalty box and he picked himself up to send Ripley the wrong way and equalise for the Bantams.
Fane was replaced minutes later by Ollie Banks as Robinson’s men looked to recover from the set back of the equaliser.
Meredith forced a smart save from Ripley after the goalkeeper palmed away his powerful effort from the edge of the box.
Latics were finding chances hard to come by but Banks played an excellent through ball to Flynn on the left with 20 minutes remaining but his low cross could not find an onrushing Latics player.
Whilst Bradford were enjoying a lot of the possession in the final 15 minutes of the game, they did not test Ripley who had been excellent all afternoon in Athletic’s goal.
The Bantams did have the ball in the back of the net in the final few minutes but the linesman adjudged Vincent Rabiega to be offside.
Latics battled until the end but could not snatch the winning goal as the points were shared.
Bradford City: Doyle, Meredith, Law, Vincelot, Dieng, Clarke, Hiwula (Rabiega 77’), Cullen, Knight-Percival, Devine.
Subs not used: Sattelmaier, Darby, Morais, Webb-Foster, Kilgallon, Boateng.
Oldham Athletic: Ripley, Law, Burgess, Clarke, Dunne, Klok, Fane (Banks 60’), Green, Flynn, Erwin (McLaughlin 70’), Mckay (Osei 88’).
Subs not used: Kettings, Wilson, Croft, Cassidy.
Goals: Bradford City (Clarke 57’) 1-1 Oldham Athletic (Clarke 5’)
Attendance: 17,793 (685 visiting supporters)