A first Posh goal from Nicky Ajose - scored three-and-a-half years after he arrived at the club - helped to clinch a first victory of 2014 for a team who have been in freefall.
Ajose, who was making only a fourth starting appearance for the club, hit the second goal with 15 minutes remaining when converting a Danny Swanson delivery in the box.
Top-scorer Britt Assombalonga did the rest of the damage to reach the 20-goal milestone in his debut Posh season.
He earned and converted a fifth-minute penalty before tucking away a late clincher after Swanson and Ajose had been involved in a slick build-up.
Three priceless points were enough to see Posh climb back into the play-off places in the first match since chairman Darragh MacAnthony delivered his public backing to under-fire boss Ferguson.
Ferguson said: "My players deserved credit for showing a lot of character.
"One victory is not enough to turn the corner, but everyone could see the commitment of the players.
"It was great to see both my strikers score. Nicky has that knack of nicking a goal and he had a good scoring record at Swindon while it is no mean feat for Britt to have reached 20 goals by this stage of the season.
"Life is full of challenges in football and it is how you come through them that matters.
"The season is very much still alive and enjoying success this way would no doubt be even more satisfying than running away with it."