An entertaining game saw Enoch Andoh net his first goal for Vale when he tapped in Byron Moore's cross.
The hosts should have doubled their lead from the spot, but Ben Alnwick's fine save denied Michael O'Connor.
Posh levelled when Michael Bostwick rifled his penalty down the middle, before Sam Foley saw his late penalty hit the crossbar.
Port Vale wasted two second-half penalties and conceded from the spot as they were held at home by Peterborough.