The Sky Blues hit back well after a disappointing first half to clinch the victory thanks to goals by Graham Barrett and Dele Adebola.
Coventry's Michael Doyle saw his early long-range effort fly over the bar while at the other end Andly Legg fired two efforts wide.
Legg continued to be a thorn in the Sky Blues defence and when he burst down the left-hand side he crossed for new signing Chris Kanu to see his half-volley brilliantly saved by Scott Shearer in the Coventry goal.
Andy Morrell came on as a second-half substitute for Gary McAllister's side and his introduction changed the match.
He immediately set up Patrick Suffo who saw his first-time effort saved by Mark Tyler in the Posh goal.
After incessant pressure Coventry finally took the lead with a great goal from Barrett in the 63rd minute.
The former Arsenal youngster hammered a 25-yard effort past Tyler to finally break the deadlock.
Just four minutes later the tie was safe as Safri played a quick free kick to Morrell and the former Wrexham striker set up Dele Adebola to slot home past Tyler.