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Britt Assombalonga had the best chance of the first half for Peterborough, as he played his way into the box before sending his strike just wide shortly before the break.
Robert Olejnik had to remain alert in the Peterborough goal shortly before the break when Lloyd James, who missed the first leg, tried to drive the ball in from 30 yards out, but the stopper just held on.
The visitors made a bright start to the second half as Assombalonga found his way into the penalty area, but he sliced the ball high from the edge of the box.
The Posh came within inches of taking the lead in the second half when Mark Little unleashed a strike from just inside the area, only to see his effort kept out by the post.
His missed proved costly three minutes later when the home side won a free kick just outside the box, allowing Dean Cox to unleash a powerful free kick.
His initial effort was blocked by the wall, but the ball fell kindly for the striker to take a second shot, which he volleyed into the bottom corner for his 16th goal of the campaign.
Orient came close to doubling their lead just over 10 minutes later when Shaun Batt was played in by Cox, but his finish went straight to Olejnik.
The home side seemed to put the result beyond doubt with just two minutes to go when Chris Dagnall found some space on the edge of the box before firing the ball in low for the second goal of the night.
Conor Washington pulled one back for the visitors in stoppage time to give them some late hope, but they were unable to find the target again on the final minutes.
Orient will face either Preston North End or Rotherham United in the final at Wembley later this month.