Centre Stuart Littler bagged a hat-trick of tries for the City Reds, but the scores were locked a 28-28 in the final minutes after a late score by Pat Weisner.
Paul scored with virtually the last kick of the game to snatch the victory.
A win over Huddersfield handed Hull their seventh straight engage Super League success, moving them into third place in the process.
In a low scoring encounter, Hull struggled to a 19-6 victory thanks to tries from Sid Domic, Richard Horne and Nathan Blacklock.
Keith Mason registered the only score for the visitors.
Warrington consolidated their position in the engage Super League play-off places with a comfortable victory over Castleford at the Halliwell Jones Stadium.
Castleford took an early lead but Warrington replied with five first-half tries to establish a 26-6 half-time lead.
The visitors threatened a comeback in the second half but they were unable to keep out the Wolves, with Brent Grose scoring two of their eight tries.
Sean Long inspired St Helens to a 28-14 Super League victory over Wigan at the JJB Stadium on Saturday night.
Jamie Lyon got the Saints first try after 23 minutes before Francis Meli extended their lead.
Wigan came back from 14-0 down at half-time with tries from Gareth Hock and Pat Richards, but Ade Gardner and Willie Talau put the game beyond Wigan before a late Brett Dallas consolation.
Stacey Jones made a tryscoring return for Catalans Dragons as the French side held off a Wakefield comeback to notch their fifth engage Super League win by a 28-20 scoreline.
Kiwi scrum-half Jones, out since February with a broken arm, claimed the first try after 22 minutes and team-mates Jamal Fakir and Laurent Frayssinous also crossed in Perpignan.
Wakefield hit back in the second half with Paul White scoring twice and Ben Jeffries touching down, but Adel Fellous and Frayssinous with his second try sealed the Dragons' win.
On Friday night Leeds rediscovered top form with a dominant second-half display to stun Bradford 30-0 at Odsal.
The Rhinos found their scoring touch with four tries in 35 minutes to turn a tight, tense contest into a flattering victory which enabled them to pull three points clear of the champions.
Rob Burrows, Willie Poching, Chev Walker, Ryan Bailey and Keith Senior got the tries while skipper Kevin Sinfield converted every kick.