Ajose found the net in the 75th minute of just his fourth starting appearance as Posh completed a hat-trick of wins over Rovers this season and pocketed their first points of 2014.
Top scorer Britt Assombalonga did the rest of the damage to reach the 20-goal milestone in his debut season in Posh colours.
Assombalonga had provided the perfect start for his out-of-form side when earning and converting a fifth-minute penalty.
Rovers were denied a leveller early in the second half when a Matthew Kennedy shot crashed against the far post before rebounding into the grateful arms of debutant Posh keeper Joe Day.
Posh saw a second goal disallowed when referee Gavin Ward ruled out Shaun Brisley's header from substitute Grant McCann's corner for a foul.
But Darren Ferguson's men only had to wait a couple of minutes to seal the points as Ajose converted a Danny Swanson delivery before creating a third goal for Assombalonga with three minutes to go.