The point took the Bulls a step nearer the play-offs, but with their promotion rivals winning on the day, their hold on second place looks less strong than it did at the start of play.
Rob Purdie gave Hereford the lead in the 77th minute after a handling offence by Anwar Uddin but Glen Southam levelled six minutes later.
First-half chances were at a premium as the sides struggled to come to terms with a blustery wind.
Craig Stanley and Dean Beckwith both got their heads to crosses from Alex Jeannin in the early stages, but without causing much threat to Tony Roberts in the Dagenham goal.
The best chance of the half arrived on 36 minutes when Daryl Taylor pulled the ball back from the right to Jamie Pitman, who sent a shot flashing a yard wide of Roberts' goal.
Three minutes later Dagenham almost netted a surprise opener. Scott Griffiths crossed from the left and Sam Saunders nipped in with a header which forced a diving save from Hereford's Wayne Brown.
The Bulls had the better of the play in the second period, forcing nine corners, and it was from the eighth of these that the goal finally arrived.
Uddin was adjudged to have handled in the melee which followed Jeannin's flag-kick and Purdie sent Roberts the wrong way to convert from the spot.
Six minutes later, Beckwith was ruled to have pulled back Griffiths at the other end and Southam had little problem in netting from 12 yards.
In the closing stages, substitute Paul Benson almost grabbed an unlikely win for the Daggers but pulled his shot across goal and wide.