Lee Tomlin's stinging drive hit the post, but the visitors deservedly went in front in the 29th minute when Tomlin got past Simon Francis and ran into the area before unleashing a curling shot beyond the reach of Addicks goalkeeper Rob Elliot.
Craig Mackail-Smith headed wide when unmarked early in the second half and paid the price for his miss as Charlton came from behind to go in front.
The equaliser arrived on the 57th minute when Johnnie Jackson headed home Francis's cross.
Charlton took the lead two minutes later as Nathan Eccleston set up strike partner Bradley Wright-Phillips for his third goal in as many games.
Pawel Abbott's 80th-minute volley was deflected past Posh goalkeeper Joe Lewis for the Addicks' third and although Mackail-Smith pulled one back in stoppage time, Charlton maintained their 100% record under boss Chris Powell.