Two goals in the space of six first-half minutes set Darren Ferguson's men on the way to a vital three points - but they had to survive a late rally by the Bantams to pocket the points.
Full-back Kgosi Ntlhe opened the scoring in spectacular style with a swerving 30-yard blockbuster in the 18th minute after a Lee Tomlin corner had been cleared into his path.
Posh's leading scorer Britt Assombalonga quickly doubled the advantage with a fine turn and finish from the edge of the box to claim his 17th goal of the season, but any thoughts of a comfortable cruise to victory were dispelled when two Bradford substitutes combined to halve the visitor's arrears with 14 minutes remaining.
The impressive Kyel Reid charged down a Mark Little clearance and delivered a pass for Andy Gray to register his first goal for 15 months by steering a shot through the legs of goalkeeper Bobby Olejnik.
Bradford almost bagged a leveller moments later when a Mark Yeates shot was well saved before Nahki Wells' follow-up was blocked by Posh skipper Michael Bostwick.
Assombalonga and Tomlin fluffed glorious chances to confirm Peterborough's success in stoppage time, but two goals proved enough to extend Bradford's poor run to one win in 12 matches.