It meant Darren Ferguson's Posh have failed to win their first seven games in the season, which equals the worst start to a campaign in the club's history.
Peterborough threatened first when Robbie Neilson's misplaced header allowed Craig Mackail-Smith a free shot at goal but Chris Weale made a comfortable save.
Lee Frecklington then fired just over from 20 yards as Peterborough continued to prosper.
In contrast, City's first real chance didn't arrive until 20 minutes when a defensive mix-up by Joe Lewis and Gaby Zakuani allowed Fryatt to feed Dany N'Guessan who drove narrowly wide.
But it was Peterborough who continued to shine with Aaron McLean giving Wayne Brown the slip before he fired into the side netting.
Posh were in front on 31 minutes when they won a penalty after McLean and Brown tangled inside the box.
George Boyd stepped up, tucked away the spot-kick low to his right with the keeper diving the wrong way.
City hit back with a Steven Howard header from Bruno Berner's cross which Craig Morgan was forced to head off the line, before Howard set-up Fryatt who blazed horribly wide from 12 yards.
Lewis then twice denied Paul Gallagher, first when he clawed away from beneath the bar an edge of the box drive and then diving low to block a 12-yard shot from the same player.
The half time substitutions of Aleksandar Tunchev and Andy King for Brown and N'Guessan galvanised City who levelled on 47 minutes when Tom Williams handled inside the area after Neilson had helped on a Gallagher shot which struck the bar.
Fryatt coolly swept home the spot-kick low to his left for his sixth strike in nine games.
Thereafter goal mouth action was at a premium as Posh withstood City's increasingly blunt attacks.
And Peterborough almost stole it in time added on when a 20-yard drive from substitute Paul Coutts flew just wide.