Brighton ended a run of 12 straight league defeats with an eventful victory.
Simon Rodger celebrated his debut for Steve Coppell's strugglers with a spectacular goal in between two Bobby Zamora penalties.
The Seagulls finished the match with ten men, goalkeeper Michels Kuipers receiving his marching orders in the closing stages after conceding a spot kick.
Brighton, numbed by a 5-0 defeat at arch rivals Crystal Palace in their previous match, went ahead in the ninth minute.
Gus Uhlenbeek, Bradford's Dutch right-back, brought down Paul Brooker and Zamora scored from the resulting penalty.
Rodger, rejected by Brighton as a schoolboy for being too small, doubled the advantage in the 42nd minute when Zamora set him up for a left-foot shot into the roof of the net from 20 yards.
Brighton should have been further in front at the break. Zamora was denied in a one-on- one by Bradford keeper Steve Banks and he also headed over a good chance from a Brooker cross.
Sheffield United recovered from 2-0 down at half time to win 4-2 in Coppell's first game in charge and the rain-drenched fans feared a repeat when City halved their arrears after 49 minutes.
Andy Gray was left unmarked as he headed in a free kick from Paul Evans.
Zamora restored Brighton's two-goal cushion five minutes later, slotting in his second penalty after Wayne Jacobs had pushed over Graham Barrett.
The Seagulls still had to sweat for their first points since August 13 after Rodger hobbled off with an ankle injury.
Kuipers brought down Stephen Warnock on the stroke of full time and he was sent off, so Brighton replaced Brooker with substitute keeper Andy Petterson.
He could do nothing about Gray's ensuing penalty, but it came too late for Bradford to avoid a fifth successive away defeat in the league