Oster pounced after frontman Billy Sharp had drilled across the face of goal, to halt Posh's recent revival that had given them hope of an making an incredible recovery in the final weeks of the season.
Peterborough hit the front 10 minutes after the break as they went in search of a third straight victory when Charlie Lee nodded home from a Tommy Rowe corner.
They had been the better side at that stage with Rovers veteran goalkeeper Neil Sullivan making fine saves to deny Sergio Torres and Lee.
But O'Driscoll's men had clearly failed to read the script as they came from behind to pinch the points.
Captain Gareth Roberts volleyed a classy 67th-minute leveller after a Martin Woods cross had been cleared into his path.
Oster then found himself in the right place at the right time to complete the turnaround and secure a result which leaves Rovers dreaming of a late charge for the play-offs and their unlucky victims appearing doomed.
O'Driscoll said: "It was always going to be tough work with only two players above six feet tall against a team who excel in set-pieces and at long throws.
"But we stuck in there after going behind, continued to play our football and got the equalising goal we deserved. Adding a winner at the end was a nice bonus.
"I'm really happy for John to get his first goal for the club. He has been asked to play with much more responsibility of late and it is a role he has relished."
O'Driscoll also hailed veteran goalkeeper Sullivan, saying: "Some people might think your reactions start to go when you are 40 but Neil proved there is nothing wrong with his when making some terrific saves."
Posh manager Jim Gannon, who is only committed to the club until the end of the season, held talks over his future with chairman Darragh MacAnthony on the eve of the game.
Gannon said: "We had problems with injuries before and during the game, but we had the chances and couldn't quite convert them.
"I had a very constructive and enjoyable meeting with the chairman and with Barry (Fry) and I have to say the club is very lucky to have two passionate football people in charge.
"I now have a good feel for the club. I haven't made a definitive decision yet, but things should be clearer in my mind within a couple of days once I have spoken to the people I want to discuss things with.
"It was an easy decision to come here on a short-term basis but it will be a much more difficult one to make now."