The Championship opened the scoring from the penalty spot through Siriki Dembele.
Posh's joy was short-lived, however, as Tammy Abraham soon equalised and, just before half-time, Christian Pulisic put Chelsea into the lead by winning and then converting his own spot kick.
It was all change at the break, with the likes of Ruben Loftus-Cheek, Armando Broja, Conor Gallagher, Baba Rahman and Ziyech all coming on.
Ziyech made the most of his runout with three goals, with Armando Broja making it six for the Blues.
With Edouard Mendy and Kepa Arrizabalaga given the afternoon off, Jamie Cumming played in goal for the first 60 minutes before Lucas Bergstrom saw the game out.