Russell Slade's side will now face either Preston North End or Rotherham United at Wembley later this month, with a place in the Championship up for grabs, after they secured a 3-2 aggregate win.
Orient took momentum into the match after securing a 1-1 draw in Saturday's first leg, courtesy of Moses Odubajo's second-half equaliser.
And after a goalless first half, Dean Cox gave the victors the lead in stunning fashion on the hour.
Cox reacted quickly after his free-kick was blocked by Peterborough defender Jack Baldwin, thrashing a volley beyond goalkeeper Robert Olejnik to delight the Matchroom Stadium crowd.
Peterborough pressed for an equaliser, but were found wanting at the back when Shaun Batt charged to the byline and cut back for Chris Dagnall.
And the substitute finished coolly with just one minute of normal time remaining to put Orient on the verge of reaching the final.
Orient did have to suffer a nervy finish, though, after a clever Conor Washington strike in the 92nd minute gave Peterborough a lifeline.
And a 96th-minute corner went over a sea of bodies and fell invitingly for defender Craig Alcock, who agonisingly saw the ball strike his knee and sail over the bar.
Orient did hold on for victory, though, as they moved a step closer to being part of English football's second tier for the first time since 1982.
