Bradford (20) 36
Tries: Lynch, Sykes, Tadulala 2, Hape, Newton, Cook Goals: Harris 4
Hull (12) 22
Tries: Houghton, Yeaman 2, Manu Goals: Tickle 3
Bradford scored seven tries to end a run of four straight defeats and climb back into Super League's top six.
Tries from Andy Lynch, Paul Sykes, Semi Tadulala and Shontayne Hape helped them into a 20-12 lead at the break.
Danny Houghton and Kirk Yeaman crossed for first-half tries to give Hull some hope at Odsal.
But Terry Newton and Tadulala took Bradford well clear and although Hull fought back through Willie Manu and Yeaman, Matt Cook had the last word.
Bradford had an explosive start with three tries in the opening 12 minutes.
Lynch took Newton's short pass to crash over for the first, centre Sykes jinked his way over for the second while a long pass by David Solomona enabled Tadulala to touch down.
Houghton responded for the visitors when he took advantage of a slip on the greasy turf by full-back Michael Platt to score.
Hape did hit back for Bradford but Yeaman reduced the deficit with a try just before the break.
Hull could have got even closer but Yeaman failed to deliver the final pass to Tom Briscoe when in the clear and in a separate move, putting a foot in touch just before he crossed the line.
Bradford made the most of their reprieves by scoring two further tries in four minutes to ease into a comfortable 30-12 lead.
Tadulala took Hape's pass for his second try and Ben Jeffries released Platt who sent the supporting Newton over for Bradford's sixth try.
Hull never gave up however and second-rower Willie Manu finished off a fine 50m-move while Yeaman then grabbed his second after intercepting substitute Craig Kopczak's pass.
But Cook ended any hopes of a comeback when he forced his way over from close range four minutes from the end.
Bradford coach Steve McNamara:
"We needed to win for our own reasons, not because of the Challenge Cup. We found a way to win eventually, which was good.
"I hate saying it but the result was probably more important than the performance. We were anxious today. We probably looked like a petrol car with diesel in the tank.
"Now we've got that off our back and the fact that the players can relax a little bit more will hopefully see a completely different side. I'm really pleased for the team because they deserved to win."
Hull coach Richard Agar:
"We did our best to make up for the start and were only a fraction away from doing it but eventually it proved too much to claw back.
"We spoke about getting off to a good start and obviously that didn't happen and it cost us.
"But we are playing a little bit more adventurously. We scored 22 points and were only better execution away from scoring a few more so there are positives.
"I thought the senior players were great. It was only the second time in Matt Sing's career that he has played at full-back and the previous time was 12 years ago but I thought his performance and effort was outstanding."
Bradford: Platt, Halley, Sykes, Hape, Tadulala, Harris, Jeffries, Vagana, Newton, Lynch, Solomona, Burgess, Langley.
Replacements: Kopczak, Finnigan, Cook, Evans.
Hull: Hall, Sing, Yeaman, Broughton, Briscoe, Washbrook, Berrigan, Dowes, Houghton, Carvell, Manu, Radford, Tickle.
Replacements: Thackray, Dale, Burnett, Wheeldon.
Referee: I Smith (Oldham)