A quick-fire brace from Sam Baldock put City in command at London Road and they held on to their advantage despite having to soak up a torrent of Posh pressure following the dismissal of Adam El-Abd.
Baldock broke the deadlock in the 10th minute with a simple finish after Brendan Moloney had headed a Wade Elliott cross back into the danger area.
And Baldock was left with another easy task six minutes later after Elliott had beaten Posh keeper Bobby Olejnik to a Jay Emmanuel-Thomas flick and hooked the ball across the face of goal.
City's dominance was thrown into jeopardy when centre-back El-Abd was shown a red card by referee Andy Woolmer after 20 minutes following an off-the-ball clash with Posh striker Britt Assombalonga.
Posh halved their arrears in the final minute of the first half when Michael Bostwick glanced in a Grant McCann corner - their first effort on target.
The home side predictably bossed the second period, but could not turn their possession into further goals.
Assombalonga, Bostwick and Nicky Ajose were all denied by smart Frank Fielding saves as City clung on to take maximum points.