Darren Ferguson's side were the first to reveal their attacking intent when a shot from Danny Swanson within the first two minutes brought a desperate block from Ipswich's Guirane N'Daw.
Ipswich had barely got out of the blocks but at last made their presence felt after 18 minutes when Aaron Cresswell's effort from more than 35 yards out cleared the crossbar.
Mick McCarthy's side were considerably closer to breaking the deadlock only two minutes later when Andy Drury's shot from 20 yards brought a timely block from Gabriel Zakuani.
The visitors were at last starting to put themselves about and Frank Nouble was unlucky to see his shot from distance rebound from the woodwork after 26 minutes.
Jay Tabb also went close for the Tractor Boys with a 12-yard effort following a corner from Drury as the increasingly adventurous visitors started to turn the screw.
Nouble then went close twice within a minute. First he brought a fabulous save out of Robert Olejnik in the Peterborough goal following a shot from the left of the penalty area, and then his header from another Drury corner narrowly missed the target.
Ferguson's side had their backs to the wall and Olejnik had to save again from a Nouble header six minutes from the break.
But Peterborough were a different proposition just after the break. Swanson's shot was blocked by Drury and, with Ipswich on the back foot, Tommy Smith had to put his body in the way of a Nathaniel Mendez-Laing shot from 12 yards.
The hosts went close shortly after the hour when Tommy Rowe's 20-yard effort brought out the best in Ipswich keeper Stephen Henderson.
Posh sensed Ipswich were there for the taking as Ferguson made a triple substitution after 68 minutes with Mendez-Laing replaced by Joe Newell, Grant McCann giving way to Kgosi Ntlhe and Tyrone Barnett entering the action at the expense of Swanson.
It was a bold move by the hosts and Ipswich too made a change with Aaron Mclean replacing Nouble before Drury gave way to Jay Emmanuel-Thomas. But a draw was a fair result as both sides struggled for precision in front of goal.