Slade's side turned in a stunning display after falling behind against the run of play when skipper Tommy Rowe edged Posh ahead in scruffy style in the 26th minute.
But class soon prevailed as three goals in the space of 20 minutes transformed the game.
A classy brace from hot-shot David Mooney sandwiched a stylish Dean Cox strike as Slade's side ran riot.
Mooney had thumped the crossbar with a dipping volley before firing Orient level on the turn seven minutes before the break.
Slade said: "You have to go away very, very happy after a 3-1 win at Peterborough.
"It was a big game for both clubs and the fact we overcame the size of the occasion and embraced it was very pleasing.
"We came through a big test very well despite going a goal down against the run of play.
"We never panic if we fall behind though.
"We stayed in control of the game, managed to create chances throughout the game and got the three points.
"We have a really rounded group of players who know that we have to continue to strive for improvement.
"The challenge is to keep doing exactly what we're doing."