The two sides cancelled each other out for the third successive meeting to continue their respective struggles in front of goal.
It was a fourth blank in five games for a Posh side whose play-off challenge is fast fizzling out while Walsall failed to find the net for a fourth successive match.
Half-time substitute Harry Anderson and striker Luke James both forced fine saves from visiting goalkeeper Richard O’Donnell as Peterborough finished strongly.
O’Donnell had also denied David Norris a first Posh goal in the opening half while a Jon Taylor cross-shot flashed across the face of goal.
Midfielder Michael Cain posed the most threat for Walsall with a series of efforts on goal. He guided a half-volley and a side-foot effort from the edge of the box wide in the first half before steering a shot just past the post with five minutes remaining.