That completed an impressive turnaround and a confidence-boosting victory as Posh reached the third round for the first time since 1993/94.
Posh's horrible habit of conceding early goals reared its head again when Tamas Priskin struck in the 14th minute.
The lively Hungarian coolly converted a right-wing cross from the returning Pablo Counago with a neat near-post finish.
The delight of breaking his Tractor Boys duck soon turned to despair when Priskin saw a 25th minute penalty - which he had won when being upended by Posh centre-back Gaby Zakuani - saved by Joe Lewis.
The Posh keeper looked suspiciously off his line when guessing the right way, but controversial referee Rob Shoebridge was unmoved.
The whistle-blower made his return from a two-game suspension for failing to spot a Crystal Palace goal in a recent Championship clash at Bristol City.
His vision was again called into question at London Road. Shoebridge blotted his copybook by booking Ipswich skipper Alex Bruce for a splendid tackle and then allowed visiting defender Damien Delaney to walk away without punishment for twice shoving Russell Martin.
That penalty save proved to be a turning point as Posh began to pour forward and soon equalised courtesy of a stunning 25-yard strike from Carling Cup specialist Lee Frecklington.
The former Lincoln City midfielder's only previous starting appearance and goal this season also came in this competition.
And just like Priskin before him, Frecklington followed up a goal by missing a glorious chance.
His came in the 38th minute when Boyd and Craig Mackail-Smith both dummied a smashing Aaron McLean cross only for Frecklington to slice his shot wide.
Chances were few and far between in the second period and Boyd's blast past Wright proved pivotal.
The Ipswich keeper did spare his side from a heavier defeat when saving superbly from McLean soon after the 64th minute clincher.