Latics dominated a lot of the game creating plenty of chances but the best fell to the Crystal Palace loanee with only a minute remaining.
The striker rose at the back post but his header smashed the crossbar and Athletic could not force the ball over the line as it ended goalless at SportsDirect.com
Stephen Robinson brought a number of players back into the starting fold after rests in midweek.
Peter Clarke and Cameron Dummigan were restored to the team in defence whilst Lee Erwin came back in attack for Latics.
It was a quiet opening to the game with both sides enjoying spells of possession.
The first effort did come from the visitors on 11 minutes as Jake Reeves curled towards Connor Ripley’s far post but his strike was wide of the goal.
Dean Parrett was the next to go close for AFC Wimbledon but Ripley comfortably saved his effort from the edge of the box.
Latics were getting a lot of joy down the right hand side with Cameron Dummigan and Ryan McLaughlin causing constant problems.
The pair combined on midway through the first half as McLaughlin crossed to the back post but it was just over the head of striker Erwin.
A minute later Dummigan and McLaughlin would again combine to set up striker Billy Mckay from six yards but James Shea in the AFC Wimbledon goal saved well with his feet.
Just before the half hour mark, Athletic again went close as Ryan Flynn’s cross found Mckay inside the penalty area but Shea again saved his effort.
The visitors had two chances to open the scoring soon after with Lyle Taylor and Reeves both going close.
Firstly Taylor smashed the side netting on the volley from 18 yards whilst a minute later Reeves was presented with acres of space but Ripley dived at his feet and denied the midfielder.
Latics put the pressure on in the final minutes of the first half as McLaughlin found Erwin at the back post but Shea again had to push aside his headed effort.
Neither side made a change at the break and it would be the Dons who first went closest in the second half.
Taylor was presented with space in the penalty area but Peter Clarke threw his body on the line and deflected his shot away from danger.
Athletic were living dangerously as the visitors again went close but Ripley pulled off a great save in a goalmouth scramble.
Robinson brought on Lee Croft in place of Erwin on 53 minutes and Athletic were almost ahead a minute later.
McLaughlin beat his man, crossed into the box but the onrushing Flynn could not connect with his header.
On the hour mark, AFC Wimbledon had a great opportunity to take the lead as Banks fouled Andy Barcham 25 yards from goal.
Dean Parrett stepped up, struck it over the wall but curled it past the far post.
Whilst both sides were enjoying spells of possession, neither were creating clear cut chances on goal.
Athletic played with good energy with Flynn and McLaughlin at the heart of the action.
With 20 minutes remaining, the two combined as the latter tried to flash a cross across the box but it was just cleared.
Chris Whelpdale’s strike tested the palms of Ripley minutes later but Athletic started to have the better chances in the final 15 minutes.
Croft’s well crafted cross was towards Clarke at the back post but it was just nodded behind for a corner before he could get a clean connection on the ball.
Latics continued to create chances as a short free kick found Flynn racing into the penalty box, his cut back found Banks who struck from distance but Shea made a great save.
Athletic thought they had won the game in the final minute of the game as substitute Ladapo struck the crossbar from close range with a header.
Suggestions it crossed the line were waved away by the referee, whilst from the rebound Clarke headed past the post.
Deep into additional time, Croft opened fire from 25 yards which Shea beat away from his goal as Latics had to settle for a point.
Oldham Athletic: Ripley, Dummigan, Clarke, Burgess, Dunne, Fane, Banks, McLaughlin, Flynn, Erwin (Croft 53’), Mckay (Ladapo 66’).
Subs not used: Kettings, Law, Wilson, Winchester, Osei.
AFC Wimbledon: Shea, Fuller, Bulman, Robinson, Francomb, Reeves, Elliott (Barnett 85’), Barcham (Whelpdale 74’), Parrett (Poleon 78’), Taylor, Robertson.
Subs not used: McDonnell, Nightingale, Egan, Owens.
Goals: Oldham Athletic 0-0 AFC Wimbledon