Max Power gave the visitors the lead 10 minutes before the half time break but the game turned on its head on 70 minutes as Jordan Flores was dismissed.
Three minutes later, substitute Dominic Poleon equalised for Dunn’s side but after late pressure, they could not force a winner.
Dunn made three changes to the starting 11 in his first home game in charge as he brought captain Liam Kelly back into the side after a recent injury.
It was Latics that started the brighter of the two sides, earning a corner in the opening minute of the game but Wigan goalkeeper Richard O’Donnell managed to claim the cross.
New loan signings Jay Fulton and Michael Higdon were lively in the opening stages of the game and combined to almost give Latics a ninth minute lead.
The Swansea loanee crossed onto the head of Higdon but it rebounded off the post and away from danger.
Kelly, the returning captain, went into the referees notebook on 11 minutes for a foul in the middle of the park.
Both sides settled into the game and started to enjoy spells of possession without really causing either side problems.
Just before the half hour mark, Wigan had their first chance of the game but Jordan Flores’ effort was tame and easily held by David Cornell.
The goalkeeper was forced into action two minutes later but he held onto Donervon Daniels’ cross well.
However, on 34 minutes, Wigan took the lead. Power was allowed freedom on the edge of the box and he fired past Cornell to give the visitors the lead.
Michael Jacobs almost doubled their lead two minutes later but Cornell did well to tip his effort around the post as Wigan piled on the pressure.
Heading into the final minutes of the first half, Latics almost found a way back into the game.
Danny Philliskirk held his man off, fed Connor Brown down the right hand side and after a melee in the box, Higdon forced a save from O’Donnell to win a corner for Latics.
From the resulting corner, Timothee Dieng had his shot blocked but at the other end, Cornell had to be alert to deny Chris McCann from six yards.
Latics made a strong start to the second half with Lee Croft proving to be a handful on the right hand side.
Five minutes into the half, the winger cut inside his man, gave the ball to Jones who fed Fulton to cross but the danger was just cleared.
Croft again was proving a handful on the right, this time he crossed to James Wilson but O’Donnell saved.
Dunn made a bold move and replaced his captain Kelly with Dominic Poleon on the hour mark, a move which would later prove a good decision.
On the hour mark, Jones lined up a free kick from 20 yards which he fired over the crossbar.
Poleon was starting to make a mark on the game as he put himself about in attack and shot over the crossbar on 66 minutes.
With Wigan happy to knock the ball around, the game flipped on its head on 70 minutes as Flores was sent off for Wigan.
After a hefty challenge from Fulton, Flores kicked out at the Swansea loanee and the referee had no hesitation in reaching for his back pocket to produce the red card.
That seemed to inspire the home side and they equalised three minutes later through Poleon.
Substitute Mark Yeates crossed into the centre, Higdon flicked the ball into the path of the striker who made no mistake from six yards to blast Latics level.
The home side really piled on the pressure after the goal and two minutes later almost took the lead.
Higdon, who proved a handful in attack, again knocked the ball back to Poleon to strike but this time he dragged his shot into the side netting.
It was a much better tempo to Oldham’s play in the second half but Wigan were defending for their lives as they held on to a point.
Jones, Fulton and Poleon all had half chances to get a winner but in the final few minutes but it just was not to be for Latics as they had to settle for a point.
Oldham Athletic: Cornell, Brown, J.Wilson, Burn, Dieng, Kelly (Poleon 58’), Fulton, Croft, Jones, Philliskirk (Yeates 68’), Higdon.
Subs not used: Coleman, Winchester, B.Wilson, Stankevicius, Eckersley.
Wigan Athletic: O’Donnell, Power (Chow 80’), McCann, James, Jacobs, Peace (Kellett 85’), Hiwula (Odelusi 71’), Perkins, Barnett, Daniels, Flores (Sent Off) .
Subs not used: Jasskelainen, Murray, Grigg, Hendry.
Goals: Oldham Athletic (Poleon 73’) 1-1 Wigan Athletic (Power 34’)
Attendance: 5,482 (1,673 visiting supporters)