Jo Kuffour was Brentford's hero once again as his fifth goal of the season helped maintain his side's unbeaten start to the campaign.
The livewire striker stuck with a sensational overhead kick with ten minutes left to take all three points when it looked like the game would end in stalemate.
Bradford were by far the better side in the first half and should have taken an early lead after four minutes when a good run and cross by Jermaine Johnson was met by Dean Windass but he miscued his volley from eight yards out.
The visitors then made their early dominance pay when they were awarded a soft free-kick by referee Andy D'Urso.
A free-kick straight from the training ground found Windass in space. When he sliced his shot the ball fell to Marc Bridge-Wilkinson, whose attempted lob was pushed onto the bar by keeper Stuart Nelson and in the scramble Mark Bower forced the ball home.
The visitors were in complete control by the time Johnson and Windass combined again, but Johnson's final ball let him down.
Nelson kept the home side in the game with two vital saves from a Johnson strike from outside the box and a quick Windass free-kick.
Bradford had a good shout for a penalty turned down by D'Urso when Windass, who was causing the home defence all sorts of problems with his clever movement, was bundled over in the box by Adam Griffiths but the referee waved away the Bradford appeals.
Brentford were being totally outclassed in midfield with Thomas Pinault unable to influence the game and provide any service for the lively Kuffour.
Leroy Rosenior made a double swap at half-time and his side took control of the game after the break, and should have been on level terms when a Paul Brooker cross was met by Kuffour but his header hit the post. Then Matt Heywood's free-kick was just missed at the back post by Griffiths.
Brentford continued to press and got back into the game when a Brooker corner was emphatically met with a bullet header from six yards out by the unmarked full-back Kevin O'Connor.
With ten minutes to go another Brooker corner was flicked on by Heywood and Kuffour's spectacular overhead kick flew past keeper Donovan Ricketts.
Substitute Chris Moore, who made a big impact as a second-half substitute, combined again with Kuffour but his snapshot was kicked over the bar by Ricketts.
Brentford were now in total control and should have wrapped up the game in the 88th minute when a Brooker cross-shot whistled passed the back post.
The home side nearly threw away the points when they failed to deal with a long throw into the box and the unmarked Bower headed straight at the keeper when it looked easier to score.
But Kuffour's strike enabled the Bees to maintain their unbeaten start to the season and take them above Bradford in the League One table.