Bradford won the first Shay derby in eight years but did it the hard way as they earned a home fifth-round tie against Wigan.
Ultimately, they proved too good for Halifax but that certainly wasn't the case for long spells of the game as their defence once more came under the spotlight.
The Bulls eased into an early 10-0 lead through tries from former Fax man Shad Royston and Gareth Raynor.
Jim Gannon responded for the hosts but Michael Platt scored after good work from Kyle Briggs.
Sean Penkywicz scored from dummy half and Elliott Whitehead produced a superb individual try before Fax pulled within two points through Frank Watene.
A further three tries followed before the break, Patrick Ah Van and Tom Burgess scoring for Bradford before Danny Jones touched down on the stroke of half-time.
Halifax put the cat among the pigeons when Sam Barlow scored four minutes into the second half but the Bulls then put the game to bed.
Ian Sibbit and Raynor both scored before Ah Van added a penalty, his seventh goal of the day.
Bob Beswick grabbed a late consolation for the hosts.
Bulls: Shad Royston; Patrick Ah Van, Michael Platt, Chev Walker, Gareth Raynor; Kyle Briggs, Marc Herbert; Andy Lynch, Heath L'Estrange, Craig Kopczak, Elliott Whitehead, Ian Sibbit, James Donaldson. Interchange: Bryn Hargreaves, Adam O'Brien, Tom Burgess, John Bateman.
Halifax: Miles Greenwood; Paul White, Lee Paterson, Dylan Nash, Rob Worrincy; Graham Holroyd, Ben Black; Jim Gannon, Bob Beswick, Neil Cherryholme, Paul Smith, Stephen Bannister, Sam Barlow. Interchange: Danny Jones, Makali Aizue, Sean Penkywicz, Frank Watene.
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