The promotion chasers struck three times in six second-half minutes to break the resistance of Hartlepool.
The north-east club could have hit the front late in the first period when Andy Monkhouse and Antony Sweeney both squandered headers, and they paid the price for their poor finishing when Posh hit their stride after the break.
Top-scorer Craig Mackail-Smith's powerful header set them on the way in Ferguson's first home game since returning to the London Road helm. Less than 60 seconds later Tommy Rowe was on hand to double their advantage after a wickedly deflected George Boyd shot had been turned onto the bar by the legs of Hartlepool keeper Jake Kean.
Mackail-Smith then beat the offside trap to turn provider for Lee Tomlin to add a third in the 68th minute with a header from five yards.
Leon McSweeney hit the post for Hartlepool from long range before James Wesolowski added the final gloss to a resounding Posh success by driving home through a crowd in the last minute.