Brian Woodall's late strike extended Dagenham's unbeaten run to five matches at the expense of Burton in League Two.
Jacques Maghoma's superb curling effort gave keeper Chris Lewington no chance to put the Brewers ahead.
Scott Doe had a header blocked on the line by Adam Bolder for the Daggers, while Lionel Ainsworth shot straight at Lewington when well-placed.
With the visitors looking certainties for victory, Woodall struck a fine equaliser from just outside the area.
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Burton Albion caretaker manager Gary Rowett told BBC Radio Derby:
"We're disappointed by the equaliser. I would say it's a well-earned point, but I think realistically it should have been a well-earned three points. We had a well-worked game plan; we knew exactly what we were going to do.
"I said to the lads, 'let's keep it tight, because we've got great options on the bench and we can change it so it opens up and we'll get chances.' I think if you look at the game, that's exactly what happened.
"We had lots of three versus twos and a lot of people running through the middle and I just think at 1-0, if we could have just taken one of those chances, then who knows? But we've got to be realistic, that's three games and we've only conceded one goal and we've taken five points."