The high-flying hosts overcame the early dismissal of centre-back Nathaniel Knight-Percival for an elbow on Dons forward Patrick Bamford to take command of an action-packed battle.
Lee Tomlin fired them ahead from a 14th-minute penalty after Danny Swanson had been scythed down by Dean Lewington and Posh incredibly doubled their advantage when top-scorer Britt Assombalonga rifled past Dons goalkeeper David Martin from a tight angle in the 33rd minute.
Bamford and Jon Otsemobor both fluffed glorious headed chances for Dons before the break and more chances went begging after the interval as the visitors piled on the pressure.
The Dons eventually halved their arrears when substitute Izale McLeod pounced from close range after Posh keeper Bobby Olejnik, who made a string of super saves, had parried Bamford's header.
Posh's battle to hold on for victory became even tougher when Mark Little became the second player sent-off following a crude challenge on Lewington.
But Darren Ferguson's men stood strong thanks to a stunning backs-to-the-wall effort to pocket the points.