The Rams had found themselves trailing in the 23rd minute after a Posh opener was started and finished by Jonson Clarke-Harris.
But it was one-way traffic from then on as the Rams went on an almighty attacking raid scoring four times inside 16 minutes against a Posh side who had previously only conceded twice all season.
Their charge was spearheaded by veteran frontman Waghorn, who levelled with a cool volley from a Liam Thompson cross in the 29th minute before Eirin Cashin completed the turnaround with a 37th-minute header from ex-Posh man Nathaniel Mendez-Laing's delivery.
Waghorn, who returned to County for a second spell in the summer, then poked in a Mendez-Laing long shot in the 40th minute to extend the advantage.
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