The Bulls showed plenty of attacking verve as they underlined their promotion credentials and thrust their visitors further into relegation danger.
Sherjill MacDonald, who had failed to score in 25 substitute appearances for West Bromwich Albion, took only ten minutes to open his Hereford account.
The on-loan forward was perfectly placed to crack home Gary Hooper's cross after Simon Johnson had opened up the Daggers defence.
Hooper got in on the act shortly afterwards, picking up Anwar Uddin's disastrously sliced clearance, rounding Tony Roberts and sliding the ball home from a narrow angle.
Dagenham showed plenty of battling qualities and twice went close before reducing the deficit on 33 minutes.
John McCombe conceded a corner and Ben Strevens outjumped the home defence to nod in Ryan Hall's flag kick.
But Hereford came storming back and extended their lead again on the stroke of half-time.
A neat move saw Richard Rose make ground on the left and his cross was handled by Sam Saunders.
The Daggers man was booked and Johnson rifled home the Bulls' third from the penalty spot.
Hereford were quickly back on the attack after the break and Toumani Diagouraga had a fierce drive saved by Roberts.
Although it took a fine stop from Wayne Brown to prevent Jon Nurse from reducing the arrears, it seemed just a matter of time before the home side extended their lead.
And so it proved with Johnson providing a cross for MacDonald to head his second on 68 minutes.
Hooper clipped the bar when it seemed easier to score shortly afterwards and, as Hereford continued to pile forward, only an excellent stop from Roberts kept out Trevor Benjamin's chip in the dying seconds.