Early pressure by the visitors paid off on 16 minutes when skipper Mark Bodley, a one-time Barnet team-mate of Gary Phillips, scored with a glancing header following a corner. Phillips, who had a fine game for United, made a great save midway through the half, tipping over a close range Danny Shipp header.
Dagenham didn't have it all their own way however, and on 38 minutes Paul Armstrong, making his debut after signing from Stevenage, latched onto a Kevin Davies pass and shot inches wide from the edge of the box. Allan Pluckrose turned provider to Ollie Stanbridge who went close with a powerful rising drive which went narrowly over the bar.
In the second half the visitors twice made good scoring chances before increasing their lead. Phillips tipped over a spectacular Shipp volley and, after Phillips denied Junior McDougald, Steve Heffer's follow-up went well wide.
But on 64 minutes as United's defence backed off, McDougald made space for himself and fired a low shot past Phillips to make it 2-0.
United never gave up, but front runners Davies and Gary Crawshaw made little headway. In the latter stages keeper Paul Newell twice foiled efforts from Armstrong as United were unable to find a way past the division's tightest defence.