Luke Gale, Adam Sidlow, Danny Addy and Tom Olbison all crossed over as the Bulls outscored their rivals four tries to two.
Thomas Minns and James Cunningham touched down for the Broncos, who fielded four debutants.
The Bulls were docked six points in midweek after entering administration for the second time and, while they remain bottom of the table, are now only two points behind a Broncos side tipped for relegation.
The Yorkshire side's difficult week also saw their prospective new owners walk out on the club, as well as a third high-profile player in a month, following the Rugby Football League's decision to hand down their points penalty.
London suffered the withdrawal of centre Jordan Atkins during the warm-up as they handed first starts to new half-back duo Ben Farrah and Josh Drinkwater plus a third Australian - forward Nick Slyney - and Wigan loanee James Greenwood.
The visitors fell behind when Addy and Adrian Purtell combined to set Jamie Foster free down the left wing for the supporting Gale, a former Broncos player, to score beside the posts.
Foster easily added the first of his four conversions.
The Broncos were further handicapped when Tonga full-back Nesiasi Mataitonga went off injured shortly afterwards and then Mason Caton-Brown was treated for some time on the pitch before also being helped groggily to the sidelines.
Yet the Barnet-based Londoners went close when James Duckworth, the last-minute replacement for Atkins, was denied by a knock-on while fielding a diagonal kick into the corner.
Warrington loanee Danny Bridge was held up for the Bulls before Sidlow crashed onto a Matt Diskin reverse pass to help double the home side's advantage.
The Broncos hit back swiftly when Minns, on a season-long loan from Leeds, chased a Scott Moore kick into the corner and Drinkwater converted.
Just before the break Luke George dived bravely within inches after some deft handling through the Bradford ranks but suffered a heavy knock in the process and was also forced to leave the field of play.
The half almost finished in farce as Moore took advantage of Brett Kearney's slip to race towards the whitewash, only to slide over himself before what seemed a certain try.
As both sides continued to come up with frequent errors a scrappy second half remained pointless until just after the hour-mark, when James Donaldson broke clear from 40 metres out and Addy was up to score and restore the Bulls' 12-point advantage.
Bradford could have sealed things moments later but Diskin dropped a scoring pass from strong-running Olbison and the home team had other chances before Foster fumbled a Moore bomb and Cunningham pounced to give London hope.
But Gale landed a drop goal and Olbison added a well-earned try a minute from time as the Bulls clung on to what might prove to be two priceless points in their attempts to defy the improbable and avoid relegation despite their hefty points handicap.
- Sports & Recreation
- Tom Olbison
- Rugby Football League
- Danny Addy
- James Duckworth