Home side Peterborough led 2-0 until the 84th minute when Bantams left-back Kelvin Mellor found the top corner with an incredible strike from nearly 30 yards, before substitute Luca Colville equalised from the edge of the area with the help of a deflection from Posh defender Rhys Bennett.
Posh had led 2-0 at half-time thanks to Ivan Toney’s fourth goal in five matches and Siriki Dembele.
Toney’s opener came after 29 minutes following a superb counter-attack from a Bradford free-kick, which ended with Marcus Maddison finding the striker at the back post with a superb left-wing cross.
Toney then turned provider in the first minute of first-half injury time, slipping in Dembele, who sprinted clear before shooting precisely with his left foot across goal.
The second half failed to spark into life until Mellor and Colville struck late for the visitors, who sit bottom of League One.