The League Two side will fancy their chances at the replay at Victoria Road, after holding the struggling Bulls in a drab first round tie.
A scrappy first half produced little in the way of thrills although such real openings as there were fell the way of Hereford.
Andy Williams skipped along the by-line but his cross was cleared in the 12th minute.
The Williams flicked on a Richard Rose throw-in to Bradley Hudson-Odoi, whose shot on the turn flashed just wide of an upright.
Daggers' keeper Tony Roberts flew through the air to grasp a long-range drive from Rose and then was quickly off his line to block, as Williams was inches from reaching a Toumani Diagouraga through pass.
Dagenham, meanwhile were being restricted to long-range efforts, none of which troubled Bulls keeper Craig Samson.
But the visitors did produced one moment of real danger four minutes before the break, Dean Beckwith having to pull off a timely tackle to block a Ben Strevens' shot away for a corner.
If the first half had been poor, then the second was worse, with goalscoring chances proving even more elusive.
Roberts pulled off a fine save to parry a 20-yard drive from Williams just after a Kris Taylor cross had flashed across the Daggers' area, inches out of the reach of Ben Smith.
But it was Samson at the other end who needed to be at his best to prevent an upset.
The Bulls' keeper twice had to fly through the air to push away dangerous crosses from substitute Jon Nurse.
But a goal would not come at either end and the sides must do it all again in ten days' time.