Ipwich, who had added motivation after Darren Ferguson's sidewon 7-1 in the reverse fixture, led when midfielder Grant Leadbitter drilled in his third goal in his last two games.
Peterborough fielded eight players who started the drubbing at London Road but it was recent signing Tyrone Barnett who brought them level before half-time.
There were then three goals in the final 13 minutes as the game's end-to-end nature continued right up to the final whistle.
Daryl Murphy's close-range header put Ipswich back in front but moments later substitute Emile Sinclair, who had been on the pitch for just five minutes, squeezed in a leveller.
However, just two minutes later full-back Cresswell's long-range shot took a deflection to settle the game in the hosts' favour.
The match began in an attacking manner as both sides tussled for early dominance.
Michael Chopra beat the Posh offside trap inside 90 seconds but the former Sunderland striker could only head tamely straight into goalkeeper Paul Jones' arms.
The visitors went straight up the other end and George Boyd picked out Barnett who flashed a right-footed effort past a post.
Boyd himself then squandered a free header before Ipswich forward Jay Emmanuel-Thomas' curling effort was pushed just wide by Jones.
The subsequent corner provided the opening goal in the 15th minute as Leadbitter followed up last week's brace at Hull to give the hosts the lead.
Andy Drury's corner was only half-cleared and when the ball came back into the box Leadbitter drilled an effort into the bottom corner of the net.
Ferguson spoke in the week about Posh continuing with their attacking mentality and they were level in the 34th minute through Barnett.
The striker, currently on loan from Crawley but due to make a permanent switch to London Road this summer, made an intelligent run to meet Boyd's pass and he poked it past goalkeeper Alex McCarthy.
Moments later, McCarthy had to parry drives from Paul Taylor and Lee Frecklington as Posh piled on the pressure.
McCarthy's agility was on display once more as he tipped another Boyd shot past the post early in the second period.
At the other end, Carlos Edwards fizzed a ball across the box and Chopra leathered the ball towards goal but he could not keep his effort down.
He came even closer shortly afterwards when he diverted Lee Martin's long-range effort onto the crossbar.
They were back ahead when Murphy headed in from six yards after Jones had flapped at a Delaney header from Martin's corner.
But Sinclair, who had been introduced for Frecklington moments earlier, found some space between two Ipswich defenders to score, making it 2-2.
Yet Cresswell had the last laugh, his speculative effort from distance taking a wicked deflection before flying in.