Darren Ferguson's side received a huge helping hand as they recovered from a nightmare start following the dismissal of County's Ronan Murray for throwing a punch at Danny Swanson after just 15 minutes.
By then Enoch Showunmi and Murray had fired the in-form visitors into a two-goal lead but Posh's numerical advantage eventually told.
Ajose halved their arrears on the half-hour with a fine low finish before top-scorer Britt Assombalonga headed them level nine minutes into the second period with his 21st goal of the season.
Ajose completed the turnaround with 16 minutes to go with a spectacular 25-yard rocket but County stunned the home faithful as Jack Grealish drilled in a leveller from an acute angle two minutes later.
But Ajose got Posh out of jail when pouncing on a rebound in the 85th minute after Nathaniel Knight-Percival's header from a Swanson corner had been brilliantly saved by unfortunate keeper Bartosz Bialkowski as County's three-match winning run came to an end.