Two goals in three minutes early in the second half brought Hereford their first home win since the season's opening day.
But until those strikes from Steve Guinan and Danny Williams, Hereford squandered some good first-half chances and looked to be chasing the game again after Steve West's 41st minute wonder goal.
Throwing defender West into attack from the start was Dagenham boss Garry Hill's major innovation for the day.
And the move certainly paid dividends as the former Woking man nodded on Mark Rooney's cross and was then on hand to volley Mark Stein's chest down into the net from fully 30 yards past the helpless Matt Baker.
Hereford, who were without injured skipper Ian Wright, introduced loan signing from Carlisle Mick Galloway into their midfield where the former Chesterfield man had a steady debut.
The Bulls, who hadn't scored in their previous three home games, looked like extending that record in the first period when Guinan and Paul Parry, twice, failed with great opportunities.
But the goal drought finally ended after 55 minutes when Rooney failed to cut out a Williams cross and Guinan was on hand to turn Michael Rose's shot past Tony Roberts.
Three minutes later the Bulls went ahead when veteran Steve Potts allowed Parry a chance to get in a close-range shot and, although Roberts blocked the effort, Parry crossed the rebound for Williams to head in from close range.
"We're our own worst enemies at the moment," said Daggers boss Hill.
"We've gone in front with a great strike from Steve West, who did a good job as target man, but then we had a mad five minutes. Hereford didn't really cause us any problems in the first half.
"At half time we were confident that we could go on and win."