Andy Butler gave Rovers the lead midway through the first half but ten minutes later Jonathan Burn notched his first goal for the club to earn Latics a point.
Athletic started the game well with Mark Yeates causing a nuisance on the left-hand side.
The winger cut inside on four minutes but his shot went harmlessly over the crossbar from 25 yards.
There was a stoppage in play on five minutes as Doncaster striker, and last season’s League One top goalscorer, Andy Williams went off with a head injury.
They brought on Dany N’Guessan on in his place but it was Latics that continued to press the home side.
Yeates again had a sight of goal on 10 minutes but this time it was well saved by Doncaster goalkeeper Thorsten Stuckmann.
Doncaster started to come back into the game with Curtis Main having their first chance of the game on 20 minutes.
One minute later, the home side should have been ahead through James Coppinger.
The experienced midfielder was free inside the penalty area but he volleyed over the crossbar from eight yards out.
It didn’t take long for the home side to take the lead as Butler gave them the lead on 26 minutes.
Cameron Stewart’s free kick was whipped into the box and the defender latched on to the cross to steer past David Cornell’s goal.
Latics were shellshocked, especially after a positive start to the game, but it only took them 10 minutes to get back level.
Yeates’ corner into the box was headed goalwards by Burn and it went over the line according to the linesman, despite the best efforts of the defender on the post.
However, that goal was almost cancelled out only one minute later as Doncaster had two opportunities to regain the lead.
Stewart again was causing a problem from set pieces. This time, his shot struck the post and N’Guessan could not finish from the follow up.
Doncaster kept the ball alive and a wicked cross into the box was met by the head of Oscar Gobern but again it rebounded off the post and away from danger.
That seemed to inspire Latics as they finished the first half strongly, keeping possession well and attacked with intent.
Before the break, Dominic Poleon had a shot blocked by a Rovers defender and the half time whistle blew.
The home side shaded the early possession in the second half with Gobern volleying over the bar from 25 yards and N’Guessan hitting the side netting on 57 minutes.
Latics made their first change just after the hour mark as Simonas Stankevicus replaced Poleon.
However, Latics were temporarily down to ten men a minute later as goalscorer Burn was forced off the field with a head injury.
Rovers looked to capitalise on their man advantage but Coppinger’s strike from the edge of the box went wide of Cornell’s goal.
Brian Wilson, who returned from a groin injury replaced Burn with 20 minutes of the game remaining but it was Doncaster who continued to press Latics.
On 72 minutes, Doncaster could have regained their lead as N’Guessan raced past Dieng but he struck over from inside the penalty area.
Latics were really under the cosh but were defending resolutely, keeping Rovers at bay.
Butler had another header which had to be dealt with whilst N’Guessan headed over from Stewart’s free kick with less than ten minutes remaining on the clock.
With time running out, Doncaster central defender Gary McKenzie headed over the crossbar and in the final minute of additional time, Mike Jones was forced to clear off the line as Latics managed to hang on for a point in Dunn’s first game in charge.
Doncaster Rovers: Stuckmann, Coppinger (c), Butler MacKenzie, Taylor-Sinclair, Stewart, Gobern (Wellens 67’), Keegan, Evina, Main, Williams (N’Guessan 7’).
Subs not used: Marosi, Middleton, Chaplow, Mandeville, P.McKay
Oldham Athletic: Cornell, Dieng, J.Wilson, Burn (B.Wilson 70’), Brown, Croft, Winchester, Jones, Yeates (Green 82’), Philliskirk, Poleon (Stankevicus 64’).
Subs not used: Coleman, Eckersley, O’Connell, Bove.
Goals: Doncaster Rovers (Butler 26’) 1-1 Oldham Athletic (Burn 36’)
Attendance: 5,647 (625 visiting supporters)