Peterborough's England Under-21 goalkeeper Joe Lewis made two fine saves - one in each half - while Town's loanee striker Stern John had a header disallowed.
Ipswich started on top but created little in the opening quarter, before the game thankfully came to life as John and Jon Stead combined to find Jon Walters who fired over from an angle.
Grant Leadbitter came close with a deflected 25-yard drive which saw Lewis initially appearing to be wrong-footed, but the former Norwich man denied the Canaries' big rivals with a fine fingertip stop.
Peterborough then enjoyed a spell of pressure, with Craig Mackail-Smith firing wide, Chris Whelpdale saw his header easily gathered by Arran Lee-Barrett who then excelled to keep out Lee Frecklington's free header from a Whelpdale cross.
Liam Rosenior chipped a fine effort inches past the post before John headed home from a Walters cross, but he had planted both hands on the back of Scott Griffiths and the effort was rightly ruled out.
Town then had a big shout for a penalty when Damien Delaney's goalbound shot hit a hand, but it appeared accidental and ref Andy Hall ruled in Peterborough's favour.
Ipswich missed another great chance 45 seconds after the half-time whistle when John found himself unmarked eight yards out from a Rosenior cross but his mistimed his header off target.
Leadbitter saw a skimming effort fly narrowly wide before Lewis made his second tremendous save to keep out Gareth McAuley's close-range header, with the Northern Irishman skying the rebound from close in.
Both sides made changes as the second half wore on, with Keane trying an all new front pairing and Peterborough sending on Shaun Batt to add extra height to the attack, but no-one could find a way through.
Owen Garvan saw a 20-yard volley held above his head by Lewis before the visitors almost stole the points in the last minute for what would have been another cruel blow to Town.
Rosenior's clearance struck Aaron McLean but dropped perfectly into the forward's path. His shot then deflected off Rosenior to leave Lee-Barrett helpless as the ball looped off him, but Delaney scrambled back to clear off the line.
Ipswich: Lee-Barrett, Wright, Delaney, McAuley, Leadbitter, Garvan, Stead (Priskin 73), Walters (Wickham 73), John (Colback 60), Rosenior, Edwards. Unused subs: McLoughlin, Peters, Smith, Trotter.
Peterborough: Lewis, Bennett, Geohaghon, Morgan, Griffiths, Frecklington, Coutts (Diagouraga 75), Boyd, Whelpdale (Batt 68), Mclean, Mackail-Smith (Rowe 88). Unused subs: Lee, McKeown, Green, Simpson.
Attendance: 19,975
Referee: Andy Hall (W Midlands)