Simeon Akinola opened the scoring before Ivan Toney’s equaliser meant both sides entered half-time level.
After both sides made a few switches at the break, Posh substitutes Siriki Dembele and Serhat Tasdemir sealed the win in the second period.
The Bees made five changes from the side that beat Crystal Palace 6-2 on Tuesday night, including Andre Boucaud and Callum Reynolds who came in for Charlee Adams and Dan Sweeney.
The first chance of the game fell Peterborough’s way after a low cross into the box from the right flank was met by a sliding Ivan Toney but his effort could only find the Bees’ Terrace.
The hosts were then dealt a blow on 18 minutes after Ephron Mason-Clark was forced to be replaced by Medy Elito after struggling to recover from an earlier injury.
However, the Bees piled on the pressure soon after when Jack Taylor found space from just outside the box before blasting over from a tight angle.
Just a few moments later, Barnet’s pressure paid off when Akinola charged down goalkeeper Christy Pym before intercepting a clearance and stroking the ball home from close range.
The Bees could have had a second three minutes later after Harry Taylor did well to pull the ball back to brother Jack, but the latter’s effort was blocked.
Up the other end, Idris Kanu set up Toney who had a great chance to equalise from close range, but Scott Loach produced a brilliant save down to his left to force a corner.
Peterborough’s number 17 did have the ball in the net eventually though after finding the bottom corner from a 35th minute free-kick.
The visitors nearly turned the game on its head shortly before the break after a corner was met with a bullet header from Mark Beevers but his effort cannoned back off the bar.
With the scores level at the break, the Bees came out for the second half after making three changes. Adams, Dan Sparkes and a trialist came on for Harry Taylor, Elliott Johnson and Cheye Alexander.
Barnet could have regained the lead four minutes into the second period after a trialist crossed the ball in for Jack Taylor but he steered his effort past the far post. The midfielder was then replaced by fellow academy graduate Antonis Vasiliou shortly after.
Posh did put their noses in front on 54 minutes after substitute Dembele beat the offside trap to loop the ball over Loach.
Just past the hour mark and Peterborough extended their advantage to two goals after Tasdemir unleashed a long-range effort that kissed the post before finding the net.
Jack Barham, who was being readied shortly before the goal, came on for the Bees’ goal scorer Akinola at the restart.
George Boyd came on at half-time to make his second debut for Posh after re-signing during the week and he came close to making it 4-1, blasting over from distance. He then had another opportunity to find the net just after, this time he fizzed the ball wide after Dembele laid him off from a free-kick.
With just under 15 minutes to go, Peterborough summer signing Mo Eisa was played through on goal but after going shoulder-to-shoulder with Ricardo Santos, he could only blast over.
The second trialist was then given a run out as the game entered it’s final stages, replacing Boucaud.
However, the Bees couldn’t claw their way back into it and finished on the receiving end of a 3-1 loss.
Attentions now turn to Wednesday night as Darren Currie’s side welcome an Arsenal side to The Hive London.