Midfielder Lee Bell gave the visitors a 34th-minute lead with his fourth goal of the season and first for five games.
But man-of-the-match Josh Scott, back at Victoria Road after a loan spell at Ebbsfleet, equalised in the 51st minute to secure a point as Dagenham stayed 16th in the League Two table.
As early as the eighth minute Billy Kee shot wide for Burton as they started the brighter.
Calvin Zola was then denied by a smart save from Dagenham 'keeper Chris Lewington, Robbie Weir rifled wide of an upright and Alex MacDonald headed wide from Anthony O'Connor's cross.
The pressure finally told just after the half-hour mark as Bell beat Lewington with a deflected strike to give the visitors the lead.
Scott fired over six minutes before the break, but it was six minutes after the resumption that saw the forward level matters with a fine solo effort.
Kee and Weir shot wide of the target as Burton got back on top and pushed hard to get back in front.
But it was not to be and victory for Port Vale saw the Brewers drop one place in the table to third.