Gwion Edwards and Jack Marriott struck either side of the break to seemingly secure Posh victory.
Ricky Holmes’ 90th minute penalty gave the Addicks late hope and the home fans were in dreamland when Ahearne-Grant scored deep into added time to nick a point.
Peterborough survived a fourth minute scare when Grant headed Ricky Holmes’ fourth minute effort off the line.
Ben Amos’ quick thinking denied Marriott after he burst through on goal before Peterborough broke the deadlock in the 11th minute.
Marcus Maddison’s free-kick was whipped into a packed six-yard box, allowing Edwards to apply the final touch at the back post.
Mark Marshall saw his shot well saved by visiting keeper Jonathan Bond and Addicks debutant Leon Best placed a looping header just off target as the hosts tried to hit back.
Maddison’s stinging drive tested Amos early in the second half.
But it was the visitors who doubled their advantage in the 58th minute, Edwards turning provider this time with a right-wing delivery which was converted by Marriott from six yards.
Ryan Tafazolli almost gifted Charlton a route back into the game by slicing Marshall’s 77th minute cross goalwards, although fortunately Bond was alert to deal with the danger.
Edwards was denied his second of the evening when Jake Forster-Caskey hacked his 85th minute shot off the line.
However, a tense finish was set up by Holmes’ 90th minute penalty, awarded after Forster-Caskey was fouled in the box by Edwards.
And The Valley was in raptures when…