Danny Foster's header earned Dagenham & Redbridge their fourth straight win.
Foster headed home Ross Smith's cut-back on the stroke of half-time, making amends for an earlier miss when he clipped the bar from close-range.
Hereford keeper Wayne Brown did well to keep out Jon Nurse's low drive as Dagenham went close to making it 2-0.
The Bulls best chance saw Gary Hooper break free on the right and pull the ball back for Stephen Gleeson, but he shot wide from 12 yards out.
Dag & Red: Roberts, Arber, Uddin, Smith, Foster , Southam, Rainford, Gain, Griffiths, Nurse, Strevens.
Subs Not Used: Hogan, Sloma, Saunders, Taiwo, Baidoo. Goals: Foster 45.
Hereford: Brown, McClenahan, McCombe, Beckwith, Rose, Johnson (Benjamin 78), Smith (Taylor 87), Gleeson, Easton (Robinson 46), MacDonald, Hooper.
Subs Not Used: Ingham, Threlfall.
Ref: Jarnail Singh (Middlesex).