Darren Ferguson's promotion chasers had performed way below par until putting the enterprising visitors in their place with three goals in the space of 13 second half minutes.
They had sizzling striker Aaron McLean to thank for turning what appeared to a frustrating night into one to remember – the ex-Grays man took his personal goal tally into double figures with the final two goals.
The mis-firing hosts fell behind on the half-hour when Daggers frontman Paul Benson capped a lightning counter-attacking raid with a smart finish past home keeper Mark Tyler.
Murmurs of discontent could clearly be heard as the visitors held onto that lead until the final third of the game when Posh went on the rampage to seal a flattering victory.
Dean Keates shrugged off a nightmare personal performance to launch the fightback.
The summer recruit, who helped Walsall roar to the League Two title last season, had looked decidedly out of sorts for the below-par hosts until hauling them level.
Keates headed the scarcely deserved equaliser past veteran keeper Tony Roberts from point blank range in the 69th minute after Aaron Mclean had inadvertently flicked a Jamie Day delivery into his path.
If the concession of that goal had been harsh on the enterprising visitors, leaking two more in the closing stages was a really cruel dose.
Dagenham were left chasing shadows as former Daggers man Craig Mackail-Smith delivered a low cross from the left that was expertly turned home by the prolific marksman McLean.
The same attacking duo combined again in the 82nd miute to ensure that Posh escaped from this off-night with maximum points.
This time Mackail-Smith popped up on the right to release his strike-partner who cleverly fired his 11th goal of the campaign past Roberts at his near post.