Wright saw his hard hitting Chester side continue their League Two progress with comfortable two-goal victory.
Chester bounced back from a midweek FA Cup replay exit and may even be in line for a reprieve in this competition as Bury fielded an ineligible player and the FA will rule on the matter next Wednesday.
Posh should not have been surprised at Chester's direct approach as their formation and tactics were exactly the same as that employed by Wright during his nine months in charge.
Often looking bewildered at the back, Posh were two-down at the break and it would have been far worse but for the heroics of goalkeeper Mark Tyler. He denied Jamie Hand early on but was beaten in the 10th minute when Jon Walters won the race to reach a swirling cross by Chester skipper Stephen Vaughan and steered the ball into an empty goal.
Tyler stuck out a leg to deny Paul Linwood, went full stretch to divert Sean Hessey's low drive and then palmed away Gregg Blundell's effort from just inside the area.
However he was helpless when Chester doubled their lead on 37 minutes, defender Mark Arber slicing the ball into his own net after Laurence Wilson let fly from long range.
Lacking free scoring loan capture Aaron McLean through suspension, Posh struggled to penetrate and their one telling first half break ended with a vital clearance by Phil Bolland as Jude Stirling whipped a low cross into a crowded box.
Posh tried to make a fight of it after the break with Trevor Benjamin sent on to beef up the attack but Chester stood firm with Bolland commanding in the middle of a back line completed by Ashley Westwood and Linwood.
Any hopes of salvaging something ended 18 minutes from time when Tyler turned an ankle after saving yet again from Bolland. With all three subs already in action, skipper Dean Holden went between the posts as Tyler limped off and prevented Chester from doing any more damage.