Goals from Reece Burke, Keane Lewis-Potter and a Malik Wilks penalty cancelled out an early Reece Brown opener to make it four wins on the spin.
The game changed in Hull’s favour when Ethan Hamilton received his marching orders four minutes before the break.
City had struggled to get into the hotly-contested fixture and Brown slotted home on eight minutes after Matt Ingram initially saved from Sammie Szmodics to give Posh the lead.
But the Tigers levelled when Burke headed home a George Honeyman free-kick.
Hull took charge when Hamilton was sent off for a second booking after a rash challenge on Lewie Coyle.
Honeyman scuffed a shot wide with the goal gaping on 45 minutes, before Ward hit the post at the other end.
Lewis-Potter put the visitors ahead on 49 minutes after tapping in Callum Elder’s cross for his seventh of the season.
And Wilks gave City a valuable two goal cushion from the spot on 60 minutes after Honeyman was fouled by Kent.
Lewis-Potter headed tamely at Christy Pym before Lewis-Potter fired a decent chance over.
Peterborough United: Pym, Kent, Thompson, Beevers, Ward (Burrows 72), Brown, Hamilton, Butler, Dembélé, Szmodics (Mason 45), Clarke-Harris (Jade-Jones 83) Unused substitutes: Eisa, Gyollai, Reed, Kanu.
Hull City: Ingram, Coyle, Burke, Greaves, Elder, Jones, Docherty, Wilks, Honeyman, Whyte (Eaves 66), Lewis-Potter (Scott 83). Unused substitutes: Long, Emmanuel, Slater, Crowley, Smith
Referee: J Busby (England).
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