There was little to separate the two sides for the entire match but when his cross-come-shot deceived Alex Cisak in the 26th minute they took the lead.
And despite creating plenty of chances in the second half, the O’s couldn’t find a leveller, while further bad news came late on with Romain Vincelot stretchered off.
Boss Fabio Liverani made three changes to the side with Ryan Hedges missing out through injury, while Shane Lowry and Andrea Dossena were also replaced by Gary Sawyer, Scott Cuthbert and Bradley Pritchard in the starting line-up.
Also on the bench for the O’s was striker Darius Henderson after a month out through injury.
Peterborough mounted the early pressure, forcing a corner inside two minutes, but there was little else of note as both sides settled into the game.
Jon Taylor was the main outlet for Posh down the right, but the O’s dealt with everything that came their way in the opening exchanges.
Former O Gabriel Zakuani put the ball behind for an Orient corner and after only half clearing the ball, Gary Sawyer took aim from just outside the box but his effort went over the bar.
But Posh took the lead in bizarre circumstances on 26 minutes when Taylor had time and space to deliver a cross into the box.
However, his cross was caught up in the wind and deceived Alex Cisak in the O’s goal before looping into the back of the net.
It was half of very few chances, but Chris Dagnall failed to capitalise on a slip from Ricardo Santos as the defender got back and blocked the effort to make amends for his mistake.
And as the half drew to a close Aaron Mclean went close for the hosts as his header from Taylor’s cross, who had switched to the left wing, was just over the bar as Posh lead 1-0 at half time.
Peterborough again started on top, but the visitors fashioned the first real chance with some neat play down the right which worked its way into the middle as Pritchard found Mooney but his effort was saved by Ben Alwnick in the Posh goal.
The O’s were definitely brighter and another good move started by Josh Wright ended with Pritchard’s ball in to the box finding McAnuff and Alnwick did well to tip his shot behind for a corner.
Henderson came on for Mooney as the visitors looked to find an equaliser, and he almost got on the end of Josh Wright’s fierce cross after being found by a lovely pass from Luke O’Neill.
With just less than half an hour to play Liverani brought on Dean Cox for McAnuff as the O’s looked to build on a positive start to the second period.
But the hosts almost capitalised on a defensive mistake as the O’s failed to clear a looping ball and Luke James forced Cisak into a fine save and block behind for a corner.
On 71 minutes Orient launched a quick counter-attack and after Wright played in an unmarked Cox in the centre, his shot was agonisingly wide of the post.
Play was then delayed for some time with Romain Vincelot down injured and after several minutes he was stretchered off, and replaced by Marvin Bartley.
Time was ticking away but the O’s created another opportunity when the ball fell invitingly for Wright on the edge of the area, however, his volley was wide of the target.
The hosts were reduced to 10 men as the game entered 10 minutes of stoppage time as Marcus Maddison was late on O’Neill and referee Brown sent the substitute off.
Cox floated in a free-kick to the back post but Bartley was unable to get a full connection on the ball as he went behind for a goal kick.
Bostwick tried his luck from range deep into stoppage time but the effort struck the top of the bar and that proved to be the final effort as Orient lost out.
Peterborough: Alnwick, Smith, Ntlhe, Bostwick (c), Taylor (Vassell 72), Payne, Washington, Newell (Maddison 46), Mclean (James 64), Santos, Zakuani.
Substitutes: Henry, Burgess, Norris, Beautyman.
Goals: Taylor 26,
Sending-off: Maddison 90.
Orient: Cisak, Sawyer, Cuthbert (c), Baudry, O’Neill, McAnuff (Cox 64), Wright, Vincelot (Bartley 83), Pritchard, Mooney (Henderson 55), Dagnall.
Substitutes: Woods, Clarke, Simpson, Dossena.
Bookings: O’Neill 56
Attendance: 6,525 (597 Orient fans)