Leading scorer Lyle Taylor put the visitors ahead with a quarter-of-an-hour to go, racing onto a long pass from Deji Oshilaja to fire his 11th league goal of the season.
But the lead proved to be shortlived as Marcus Maddison levelled only four minutes later when providing a cool finish to a clever Jack Marriott pass.
Only a full-stretch save from Dons goalkeeper George Long prevented Posh from completing a late turnaround as he kept out a low blast from loan striker Omar Bogle.
Both sides had posed little in the way of attacking threat during a lacklustre opening half when top scorer Jack Marriott and Maddison were denied by Long, while the visitors failed to register an attempt on target.
Posh should have hit the front midway through the second half when Chris Forrester saw a looping header cleared off the line by Barry Fuller after Danny Lloyd fluffed an initial effort.
But they then found themselves behind before quickly responding as the spoils were shared.
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.