The Wolves, despite the losses of Adrian Morley, Chris Bridge, Martin Gleeson and Vinnie Anderson to injury, opened the scoring with a penalty from Lee Briers, before the half-back sent Ben Westwood over the try line.
Bradford hit back with a touch down from full-back Michael Platt, who had arrived at the club in the off-season from Castleford Tigers, but Warrington went into a 14-6 lead when Briers’ kick was touched down by Westwood.
The Bulls grabbed a decisive score just before the half-time break, Iestyn Harris sending Glen Morrison over to reduce the arrears to 14-12 at the interval.
The restart saw Bradford draw level with a Paul Deacon penalty, before Lesley Vainikolo touched down to put them ahead for the first time, and James Evans grabbed a try to extend that lead still further.
Platt then stepped up to grab his second try of the game, starting a move involving Morrison and Jamie Langley that resulted in him getting over the line himself.
Chris Leikvoll gave the Wolves a glimmer of hope with a touch down as Bradford were reduced to twelve men, but Platt crossed the line five minutes from time to complete his hat-trick and seal the win.