Jon Nurse's winner moved Dagenham and Redbridge up to fifth and extended Bradford's poor start to the season.
The only goal came when the Bantams failed to clear Gavin Tomlin's corner and the ball fell to Nurse, who drove a powerful low shot into the net.
Bradford, who have now only picked up one point from four games, had earlier seen Jack Compton's shot hit the bar.
The hosts dominated the second half but were denied an equaliser when Chris Lewington blocked Ross Hannah's effort.
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Bradford City manager Peter Jackson told BBC Radio Leeds:
"We're really disappointed to come away with nothing from the game. I felt we didn't really take the lead. We gave a sloppy goal away. We've never really in the league got ourselves in front and given ourselves something to hold on to.
"These fans are desperate for this team to succeed, and long may that continue because they can see they are young and energetic and they're desperate to do well as well.
"All of the goals we've conceded have been sloppy which is disappointing. We've not kept a clean sheet again and that's disappointing."