The Bulls clinched their first win at Headingley in almost four years to renew hopes of a late play-off charge.
Mick Potter's side edged a nervy encounter 18-12 for the club's first triumph on Leeds soil since Lesley Vainikolo's final Bradford game on June 29, 2007.
After an error-filled opening quarter, the hosts took the lead when Rob Burrow started a move that saw Ryan Hall score in the corner, Kevin Sinfield converting.
Bradford hit back in controversial fashion when Olivier Elima scored after Sinfield and Hall failed to deal with a Ben Jeffries kick.
The back-rower didn't seem to properly gain control of the ball as it bobbled in the in-goal area but Steve Ganson awarded the try.
An error from Jason Crookes allowed Leeds to extend their lead, the winger fielding Sinfield's kick but then losing the ball in a tackle from Carl Ablett.
Jamie Jones-Buchanan pounced to touch down, Sinfield again improving.
But the Bulls cut the gap before the interval, Elima scoring a well-worked try after Elliott Whitehead had flicked back Marc Herbert's crossfield kick. This time, Ah Van added the extras.
Ah Van cut the gap further with a penalty six minutes after the interval and that set the tone for the second half.
The Kiwi struck again from 35 metres just before the hour mark and again, much closer in, moments later.
Surprisingly, he hit the post with a relatively easy kick but, after his side had heroically survived a Rhinos onslaught, sealed the result with a kick in the final minute.
Bulls: Brett Kearney; Jason Crookes, Patrick Ah Van, Elliott Whitehead, Gareth Raynor; Ben Jeffries, Marc Herbert; Andy Lynch, Matt Diskin, Craig Kopczak, Jamie Langley, Ian Sibbit, Olivier Elima. Interchange: Nick Scruton, Michael Platt, Bryn Hargreaves, Danny Addy.
Rhinos: Brent Webb; Lee Smith, Brett Delaney, Carl Ablett, Ryan Hall; Kevin Sinfield, Rob Burrow; Kylie Leuluai, Danny Buderus, Jamie Peacock, Weller Hauraki, Jamie Jones-Buchanan, Chris Clarkson. Interchange: Paul McShane, Ian Kirke, Ryan Bailey, Ali Lauitiiti.
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