The prolific forward scored his sixth goal in seven matches when rifling in a 69th-minute rebound to power his side to within one point of the automatic promotion places.
Mclean finished from 10 yards to register his 16th goal of the season after Carlisle goalkeeper Ben Williams had blocked a shot from Chris Whelpdale. In the process, Mclean spared the blushes of his strike partner Craig Mackail-Smith who had fluffed a great headed chance only moments earlier.
Posh lost influential central defender Gabriel Zakuani after only nine minutes with a back injury. He landed awkwardly after an aerial challenge and required eight minutes of treatment before being stretchered off and taken to hospital.
Posh suffered a further blow just before the break when recent recruit Lee Frecklington hobbled off with a hamstring strain.
Danny Graham came closest to scoring for the visitors but he was denied from point-blank range by Posh goalkeeper Joe Lewis in the fourth minute of first-half stoppage-time.