With the two sides battling for a precious play-off spot the first half was predictably edgy - with neither team mustering a shot on goal during the first ten minutes.
Bradford thought they had broken the deadlock in the 17th minute when Peter Thorne chipped cleverly over keeper David Button from 15 yards - only for the linesman to raise his flag for offside.
Daggers felt hard done by in the 21st minute when their penalty claims were turned down after defender Paul Arnison had appeared to use his arm to block Peter Gain's strike on the line.
Dagenham skipper Mark Arber should have done better in the 36th minute when he headed an inviting Sam Saunders cross straight at keeper Rhys Evans from point-blank range.
Bradford piled on the pressure at the start of the second half - and had another goal disallowed in the 55th minute when Chris Brandon's headed effort was ruled out because of a push on Button.
The home side soaked up the pressure and hit City with a sucker-punch when Saunders found space on the edge of the area in the 57th minute before thundering an unstoppable strike past Evans to give his side the lead.
Full-back Scott Griffiths came close to doubling Dagenham's lead just two minutes later when he hammered a bullet header against the crossbar with the keeper stranded.
City piled men forward in search of an equaliser, with Lee Bullock hitting the post with a glancing header in the 77th minute.
Paul Benson settled Daggers' nerves in the 82nd minute when he ran on to a clever Ben Strevens throughball before slotting calmly under the onrushing Evans to double the lead.
Strevens rubbed salt into the wounds in the 86th minute when he pounced on a fumble by Evans to prod home the third and seal the points.