A sterling effort yielded nothing as the Bulls suffered their third straight defeat in a nervy Odsal derby.
Despite a vast improvement from the previous week's effort at Salford, Mick Potter's side came up short once more.
Bradford started in impressive fashion and opened the scoring when Patrick Ah Van touched down Marc Herbert's crossfield kick.
Andy Lynch scored three minutes later, Ah Van converting to open a 10-0 gap.
But Leeds hit back and clawed themselves level through tries from Paul McShane and Jamie Jones-Buchanan, Kevin Sinfield converting the former.
An Ah Van penalty goal edged the Bulls 12-10 in front at the break and they extended their lead when Olivier Elima touched down on 47 minutes.
Again, the Rhinos responded in fine fashion, Keith Senior's try and Sinfield's conversion pulling them level before Ryan Hall scored, Sinfield once more adding the extras.
There were still more twists and turns to come, Elima grabbing his second of the game off the delayed pass from Herbert before Ah Van's kick made it 22-22.
Sinfield kicked a penalty goal to put the visitors back in front before Danny Buderus scored to kill the game off two minutes from time.
Bulls: Shad Royston; Gareth Raynor, Michael Platt, Chev Walker, Patrick Ah Van; Brett Kearney, Marc Herbert; Andy Lynch, Heath L'Estrange, Craig Kopczak, Olivier Elima, Elliott Whitehead, James Donaldson. Interchange: Matt Diskin, Bryn Hargreaves, Tom Olbison, Tom Burgess.
Rhinos: Brent Webb; Kallum Watkins, Brett Delaney, Keith Senior, Ryan Hall; Kevin Sinfield, Rob Burrow; Luke Burgess, Danny Buderus, Kylie Leuluai, Jamie Jones-Buchanan, Chris Clarkson, Carl Ablett. Interchange: Ben Cross, Ian Kirke, Weller Hauraki, Paul McShane.
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