Russell Slade's leaders fell behind against the run of play when Grant McCann's free-kick was diverted in by Posh skipper Tommy Rowe after 26 minutes, but it did not take them long to turn the contest around.
The excellent David Mooney fired a warning shot when thumping a volley against the crossbar, but not even the woodwork could come to Posh's rescue when he beat Bobby Olejnik with a 38th-minute shot on the turn after strike-partner Kevin Lisbie had steered a cross into his path.
Both forwards were involved in the build-up as Dean Cox stylishly swept Orient ahead four minutes after the break when clipping the ball over Olejnik.
The points were in the bag in the 58th minute when Mooney collected a pass from Cox and flashed a low drive across Olejnik to register his 11th goal of the campaign and join Coventry duo Leon Clarke and Callum Wilson at the top of the League One scoring charts.
Smart saves from Olejnik denied Mooney his hat-trick and Cox a second goal, while Posh offered very little in attack.