It was a tremendous effort from Martin Ling's side, who played for 70 minutes with just 10 men after striker Paul Connor was sent off for violent conduct following a clash with Paul Carden.
Peterborough finally cut the deficit five minutes from time when substitute Lloyd Opara netted but it was too little too late as their hopes of making the play-offs suffered a major setback.
It was Orient who were quick out of the traps as they piled on the early pressure.
Lee Steele, who replaced top scorer Gary Alexander in the starting line-up, raced clear after eight minutes but his tame shot was saved by Mark Tyler in the visiting goal.
After some neat build up play Lockwood set Steele up again but the Posh goalkeeper came to the rescue.
The breakthrough came on 16 minutes when Joe Keith's cross from the left was handled by Phil Bolland and defender Lockwood stepped up to crash the ball high to Tyler's right and although the keeper got a hand to it he could not keep the ball out.
Orient threatened to run riot as a Corden free kick flew inches over and Steele then headed an Adam Tann cross just wide.
But on 20 minutes Orient striker Connor elbowed Carden in a touchline bust up and was dismissed by referee Paul Melin.
Posh tried to turn the screw with their numerical advantage and Peter Gain's 20 yard effort tested home keeper Glyn Garner.
But for all their pressure Peterborough created little and it took a spectacular save from Tyler to deny Corden stretching Orient's lead on the half hour.
Orient might have had a second penalty just before the break before Corden's delicious 20 yard drive on 70 minutes looked to have settled the issue.
But there was still time for Opara to strike 5 minutes from time when he fired home Danny Crow's pass to set up a nervous finale.