His players delivered another battling performance to edge out Cheltenham in a duo between two of League Two's play-off contenders.
Bleasdale, put in charge after manager Mark Wright was first suspended and then dismissed for gross misconduct, saw his men roll up their sleeves and defend with great determination to hang on to their slender advantage given them by a 55th minute goal from Richard Logan.
Gavin Caines rescued Cheltenham early on dispossessing Logan with a superbly timed tackle after the striker had been released by Danny Crow, but the visitors then created the better chances on a poor playing surface that made good football almost impossible.
Lee Harrison, deputising in the Posh goal for the injured Mark Tyler, did well to keep out a shot from nine-goal Town top scorer Kayode Odejayi and Harrison also saved well from Brian Wilson when the midfielder caught Andre Boucaud in possession and stormed forward.
Posh upped the pace after the break and Caines cleared from Crow at the expense of a corner which was taken short for Dean Holden to deliver a cross that Sean St Ledger glanced down for Shane Higgs to pull out of the air diving to his left.
Maintaining the momentum, Posh broke the deadlock as Logan raced onto a shrewdly placed pass from St Ledger to claim his fourth goal of the campaign, lifting the ball over Higgs as he raced off his line.
Manager John Ward reacted quickly introducing Cheltenham substitute Damian Spencer and the lanky striker almost made an immediate impact, home defender Mark Arber having to produce a fine challenge as an equaliser looked likely.
But Cheltenham's cause was not helped in the closing minutes when sub Steven Gillespie, newly signed from Bristol City was dismissed for two yellow cards in quick succession following a melee after which Wilson was also booked.