In-form County looked to be heading for a fourth consecutive win when Enoch Showunmi and Ronan Murray put them two goals to the good inside seven minutes.
Forward Murray was then sent off after 15 minutes for an altercation with Danny Swanson and his indiscipline proved costly as Peterborough made their numerical advantage pay.
Former Manchester United man Ajose pulled a goal back on the half-hour with a left-footed finish and striker Britt Assombalonga headed an equaliser early in the second half.
Ajose then found the top-right corner with a fine strike to put Darren Ferguson's side in front for the first time, but Jack Grealish made it 3-3 just over a minute later.
Ultimately it was Ajose who had the last laugh, striking from close range five minutes from time to secure all three points and move Peterborough above Rotherham United into fifth place.
In the other League One game to be played on Tuesday night, Crewe Alexandra moved out of the relegation zone with a 2-0 home win over MK Dons.
Chuks Aneke put Crewe in front and Ajay Leitch-Smith doubled the lead in the second half after Dons midfielder Shaun Williams had seen a penalty saved.
Victory for Crewe moved them up to 19th and ensured the visitors missed a chance to go eighth.
Rochdale scored twice in stoppage time to secure a 2-2 draw at fellow promotion-hopefuls Chesterfield in the only League Two game on Tuesday.
Goals from Gary Roberts and Marc Richards put Paul Cook's side on course for a victory that would have taken them above their opponents into second place.
Yet Richards then turned from hero to villain when he gave away a penalty, which was converted by Ian Henderson.
Peter Vincenti then stunned the home side when he headed an equaliser in a dramatic finale.
