Jon Nurse's 27th-minute goal secured a 1-0 win for Dagenham and condemned Bradford to their third defeat in four matches.
The relegated Daggers, by contrast, have made a great start to the campaign winning three of their first four games.
The decisive goal came after Bradford failed to clear Gavin Tomlin's left-wing corne, Sam Williams had a shot blocked in the crowded goalmouth and Nurse scored what proved to be the winning goal.
Bradford almost went in front in the third minute Jack Compton struck the crossbar.
But Dagenham's lively attack caused problems for the home defence and they should have gone ahead in the 17th minute. Bradford keeper Martin Hansen could only parry Medy Elito's cross, but Tomlin fired over the bar with the goal at his mercy.
Bradford dominated the second half in a desperate search for an equaliser but the nearest they came to scoring was three minutes from the end when Chris Lewington dived full length to turn away a well struck shot from Ross Hannah.
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