Bradford took an early lead through captain Matt Diskin but struggled to live with Hull thereafter as Gareth Ellis, Joe Westerman, Shaul, Richard Whiting, Aaron Heremaia and Danny Houghton all crossed before the break, with Adrian Purtell responding for the visitors.
Shaul grabbed his second just after half-time and Jordan Rankin got on the scoresheet before Adam Henry went over late on for the Bulls.
Whiting was preferred to Ben Crooks at centre for Hull, while Chris Tuson was handed his debut in the back row and Liam Watts made his first appearance of the season off the bench.
However, Garreth Carvell, who controversially moved from Bradford to Hull without playing a competitive match for the Bulls, remained sidelined with an ankle injury.
Bradford included new loan signings Liam Sutcliffe and Greg Burke in their 17 but were without Luke George after he suffered a concussion in last weekend's victory over London.
Traffic problems on the M62 saw last season's fixture at the KC Stadium moved from Friday to Sunday but there were no such issues on this occasion and Hull got off to the worst possible start as Tom Lineham put the kick-off out on the full.
The Bulls rolled down field from the resultant penalty and hit the front when Diskin caught the home defence napping and went over from dummy half.
Hull responded positively and levelled the match up as Heremaia put Ellis through a gaping hole on six minutes.
The home side soon forced back-to-back drop-outs and were rewarded for their persistence when Westerman forced his way over.
Shaul crossed in the next set after strong play by Fetuli Talanoa and the writing was on the wall for the Bulls.
Bradford did move to within six points of their hosts courtesy of Purtell's try in the corner in the 27th minute but Manase Manuokafoa knocked on from the restart and Whiting showed good strength to put the Black and Whites back in control.
Heremaia went under the sticks on 32 minutes after good play by Houghton before the hooker took an offload from Watts to crash over from close range to give his side a 32-10 half-time lead.
Hull were quickly into their stride in the second half and extended their advantage when Shaul pounced on Richard Horne's brilliant reverse kick to touch down.
Jordan Rankin powered over after a break in the scoring to make it 44-10 and that is the way it stayed until the Bulls grabbed a consolation four minutes from time.
An enterprising run from halfway by Sutcliffe put Bradford in a promising position on the last tackle and Luke Gale's cross-field kick was neatly helped on by Elliot Kear for Henry to score.
Jamie Foster added the extras from out wide but the damage had already been done as Hull bounced back from successive defeats on the road.
- Sports & Recreation
- Aaron Heremaia
- Joe Westerman
- Jordan Rankin
- Danny Houghton
- Gareth Ellis
- Liam Sutcliffe
- Adrian Purtell
- Matt Diskin