Following early efforts from Shaquile Coulthirst and Leonardo Da Silva Lopes, Grant McCann's side deservedly took the lead after 21 minutes with Ryan Tafazolli rising highest to nod in Paul Taylor's free-kick.
Lopes could have doubled Posh's lead just before half-time but his effort from just inside the penalty area was easily saved by Dillon Phillips.
The Addicks came out on the front foot after the break and went close through Josh Magennis, but the forward's effort ricocheted back off the inside of the far post.
To frustrate the hosts further, Jordan Botaka then saw a deflected effort loop up onto the crossbar with Luke McGee beaten in the 55th minute as Charlton searched for an equaliser.
Peterborough doubled their advantage in the 66th minute courtesy of a superb Gwion Edwards solo effort to seal an impressive away victory.
Report supplied by the Press Association
Match ends, Charlton Athletic 0, Peterborough United 2.
Second Half ends, Charlton Athletic 0, Peterborough United 2.
Attempt blocked. Chris Forrester (Peterborough United) right footed shot from outside the box is blocked.
Adam Chicksen (Charlton Athletic) is shown the yellow card.
Chris Forrester (Peterborough United) is shown the yellow card for a bad foul.
Adam Chicksen (Charlton Athletic) wins a free kick in the defensive half.
Foul by Ricardo Santos (Peterborough United).
Substitution, Peterborough United. Ricardo Santos replaces Paul Taylor.
Substitution, Peterborough United. Bradden Inman replaces Gwion Edwards.
Attempt blocked. Joe Aribo (Charlton Athletic) left footed shot from outside the box is blocked.
Corner,  Charlton Athletic. Conceded by Ryan Tafazolli.
Substitution, Charlton Athletic. Brandon Hanlan replaces Morgan Fox.
Attempt missed. Adam Chicksen (Charlton Athletic) left footed shot from the left side of the box misses to the right.
Attempt missed. Morgan Fox (Charlton Athletic) header from the centre of the box misses to the right.
Corner,  Charlton Athletic. Conceded by Michael Smith.
Attempt blocked. Ezri Konsa Ngoyo (Charlton Athletic) right footed shot from outside the box is blocked.
Attempt blocked. Jorge Teixeira (Charlton Athletic) right footed shot from the centre of the box is blocked.
Ademola Lookman (Charlton Athletic) wins a free kick in the defensive half.
Foul by Chris Forrester (Peterborough United).
Attempt missed. Chris Forrester (Peterborough United) right footed shot from outside the box misses to the right.
Foul by Patrick Bauer (Charlton Athletic).
Tom Nichols (Peterborough United) wins a free kick in the defensive half.
Ezri Konsa Ngoyo (Charlton Athletic) wins a free kick in the defensive half.
Foul by Paul Taylor (Peterborough United).
Adam Chicksen (Charlton Athletic) wins a free kick in the defensive half.
Foul by Leonardo Da Silva Lopes (Peterborough United).
Ezri Konsa Ngoyo (Charlton Athletic) wins a free kick in the defensive half.
Foul by Gwion Edwards (Peterborough United).
Attempt blocked. Leonardo Da Silva Lopes (Peterborough United) right footed shot from the right side of the box is blocked.
Substitution, Charlton Athletic. Joe Aribo replaces Fredrik Ulvestad.
Substitution, Charlton Athletic. Adam Chicksen replaces Jordan Botaka.
Attempt missed. Josh Magennis (Charlton Athletic) header from the centre of the box is high and wide to the right.
Attempt saved. George Moncur (Peterborough United) left footed shot from the centre of the box is saved in the centre of the goal.
Goal!  Charlton Athletic 0, Peterborough United 2. Gwion Edwards (Peterborough United) right footed shot from the centre of the box to the top left corner. Assisted by George Moncur.
Substitution, Peterborough United. George Moncur replaces Shaquile Coulthirst.
Foul by Andrew Crofts (Charlton Athletic).
Gwion Edwards (Peterborough United) wins a free kick in the attacking half.
Morgan Fox (Charlton Athletic) is shown the yellow card for a bad foul.
Foul by Morgan Fox (Charlton Athletic).
Leonardo Da Silva Lopes (Peterborough United) wins a free kick on the left wing.
Karl Robinson is still awaiting his first victory as Charlton boss after seeing his  new side beaten at home by play-off chasing Peterborough.