Dean Windass scored two second-half goals to rescue a point for play-off chasing Bradford at London Road.
City keeper Paul Henderson allowed Steve Thomson's shot to spin out of his grasp to gift Posh the lead before Andy Legg fired in a 25-yard free-kick.
But Windass drilled in from the edge of the box and then smashed in from a tight angle after intercepting a poor clearance from Legg to draw City level.
Nicky Summerbee almost won it for City, but his effort cleared the crossbar.
Peterborough: Tyler, St. Ledger, Burton, Arber, Ireland, Deen, Thomson, Boucaud, Legg, Willock (Clarke 74), Purser (Logan 73), Logan (Huke 82).
Subs Not Used: Coulson, Plummer.
Goals: Thomson 28, Legg 31.
Bradford: Henderson, Atherton, Wetherall, Bower, Emanuel, Summerbee, Bridge-Wilkinson, Schumacher, Muirhead (Morrison 53), Cooke (Forrest 87), Windass.
Subs Not Used: Ricketts, Symes, Armstrong.
Booked: Cooke.
Goals: Windass 64, 73.
Att: 3,472
Ref: P Melin (Surrey).