Mackail-Smith broke the deadlock nine minutes before the break when coolly slotting past Dons keeper David Martin after strike-partner Mclean had flicked the ball into his path.
But the lead was short-lived as Dean Lewington lashed the visitors level inside 60 seconds. The Dons skipper made no mistake from 10 yards after the home defence had failed to deal with a Peter Leven long throw.
But Posh soon regained the upper hand in the second period. Mclean made Dons pay for leaving him unmarked by nodding home Grant McCann’s 48th-minute corner delivery.
The Dons number one twice denied McCann and pulled off a flying stop to keep out a goalbound blast from Lee Tomlin as they survived a torrent of pressure.
And Karl Robinson’s men were guilty of squandering a great chance to level when defender Gary MacKenzie blazed over from close range with 15 minutes to go.