City asked the attacking questions in a dreadful opening half and the fact they failed to beat home goalkeeper Joe Lewis hardly mattered as Posh didn't get in as much as a single shot at the opposite end.
Bradley Orr forced Lewis to tip over with an early looping 30-yard right-footed effort and the former Newcastle full-back later got forward to fire wide when released by Nicky Maynard.
Lewis went down to his right to hold a drive from £2.25million record signing Maynard, before a mistake by Craig Mackail-Smith let in Liam Fontaine for a 20-yard blast that Lewis held well.
With manager Jim Gannon having decided not to stay with Posh beyond the end of the season, the home cause on the field was not helped when a side already giving a first league start to 17 year-old Nathan Koranteng lost midfield man Chris Whelpdale, who limped off after only 13th minutes.
Posh finally managed an effort on target just before the hour with Dean Gerken doing well to deflect Exous Geohaghon's shot following a Tommy Rowe cross.
Then Mackail-Smith whipped in a dipping effort from the left that Gerken was forced to push against the crossbar.
With substitute Kerry Gilbert, who is on loan from West Bromwich Albion, making an impact wide right, Posh again went close with Josh Simpson seeing a fierce low shot smothered by Gerken.
To the frustration of Posh, City edged decisively ahead in the 71st minute when Clarkson was perfectly positioned to claim his fourth goal of the season by nodding in at the near post from a corner by fellow Scotsman Paul Hartley.