Foster swooped to head home Ross Smith's cut back and make amends for a bad miss midway through the half when he clipped the bar from close range.
Hereford had looked like they would dominate possession from the start, although the home side fashioned the first chance with Ben Strevens heading Jon Nurse's corner over.
The Bulls showed their class too as Gary Hooper's spectacular overhead volley was narrowly off target.
It was Daggers who came closest to breaking the deadlock when Strevens got to the byline and pulled the ball back, but Foster's close-range effort hit the woodwork and went over.
Hereford also went close midway through the half when Hooper's clever pass found Simon Johnson just outside the box, but he dragged his shot wide.
Bulls keeper Wayne Brown enjoyed a huge let off on 37 minutes when he badly misjudged Strevens' looping header, but Trent McClenahan was on hand to head it off the line.
The Daggers also came close when a long throw was touched on by Nurse, but Strevens' flick was straight at Brown.
The home side's excellent spell was rewarded when Glen Southam's free-kick was met by Nurse, his effort was knocked back in by Ross Smith and Foster headed into the corner.
After the break, a lovely passing move from the Bulls led to Richard Rose having a sight of goal, but his 20-yard drive was off target.
Brown continued his inconsistent night when a poor goal-kick only reached Nurse, but he redeemed himself to produce an excellent low block.
The Bulls wasted a glorious chance on 63 minutes when Anwar Uddin slipped allowing Hooper away on the right and his inch-perfect pass was met by Stephen Gleeson just 12 yards out, but he fired wide with the goal at his mercy.
Dave Rainford headed just over for the Daggers as the home side looked for that crucial second goal, while Nurse also tested Brown again.
Sherjill MacDonald and Hooper continued to impress but, although the Bulls ended up with four strikers on the pitch, they couldn't break down a resolute home side.