Warrington struck either side of half-time to reach the Carnegie Challenge Cup quarter-finals.
Bradford were clinging to a 6-4 lead four minutes before half-time but the Wolves ran in four tries in 14 minutes. The Australian winger Joel Monaghan scored two en route to a hat-trick.
Bradford centre Adrian Purtell was denied a try for a knock-on but made amends on 12 minutes picking up a loose ball to race over following a steal by Keith Lulia. Luke Gale added the conversion, but Warrington clawed their way back with penalties. They got a Monaghan try after 22 minutes and Ben Westwood would have added a second but he placed the ball on Jamie Langley's foot.
The Wolves struck twice in the last four minutes of the half. Brett Hodgson caught the defence flat after scooping up a stray pass and Chris Riley swooped on a fumble by Bulls prop Bryn Hargreaves.
The Yorkshiremen trailed 16-6 after Hodgson's conversions, and conceded two further tries at the restart. Monaghan grabbed his second, touching down Hodgson's grubber kick, and Ryan Atkins scored from a scrum. Hodgson kicked his third to make it 26-6, but Lulia finished a six-man move.
The Wolves were reduced to 12 men on 65 minutes when Chris Hill was sin-binned and the Bulls scored a try through Olivier Elima. Gale kicked his second goal but Monaghan crossed at the corner a minute from the end to complete his hat-trick, with Hodgson taking his goal tally to four from seven.
Warrington Hodgson; Riley, Bridge, Atkins, J Monaghan; Briers, O'Brien; Hill, Higham, Wood, Waterhouse, Westwood, McCarthy. Substitutes used Harrison, Grix, Carvell, Cooper.
Bradford Pryce; Purtell, Whitehead, Lulia, Ainscough; Jeffries, Gale; Hargreaves, Diskin, Kopczak, Elima, Bateman, Langley. Substitutes used L'Estrange, Addy, Manuokafoa, Burgess.
Referee James Child (Dewsbury).Reuse content