Wayne Burnett's men had lost their previous three league and cup fixtures, but three points on Saturday saw them leap-frog their opponents in the table courtesy of goals from Zavon Hines and Luke Howell.
The Daggers went ahead after just eight minutes thanks to a hotly-contested penalty. Hines tumbled under Phil Edwards' challenge, though the visiting players claimed contact was minimal.
However, referee David Phillips gave the spot-kick and Hines smashed home his sixth goal of the season.
Medy Elito almost doubled the lead when he fizzed a shot inches wide, before Burton rallied before the interval.
Twice Robbie Weir was denied by smart saves from Chris Lewington. Adam McGurk was next to be thwarted by the Dagenham goalkeeper shortly after half-time.
The Daggers doubled their lead in the 54th minute when Hines' free-kick was clinically headed home from eight yards out by Howell.
Ian Sharps missed Burton's best chance of a late consolation goal when he drilled a shot just wide.