John Still's on-song side were made to fight for maximum points after their Yorkshire visitors bravely battled back from three-nil down to force the issue.
Bradford never levelled, but Alan Connell's late goal gave them hope they could at least snatch something from a lively contest at the London Borough of Barking and Dagenham Stadium.
Billy Bingham gave the hosts a deserved sixth-minute lead with a clinical strike before Michael Spillane doubled Dagenham's lead with a sweet effort on the half-hour mark. And it got even better for the home team when Luke Wilkinson headed home from Medy Elito's cross six minutes after the break.
But Bradford hit back when Nahki Wells scored a brace inside six minutes. The Bermuda forward first drilled a shot into the corner, before netting from the penalty spot after keeper Chris Lewington had fouled Connell.
However, 14 minutes from time Dwight Gayle restored a two-goal cushion, only for Connell to score with six minutes remaining to make things very interesting.