The first chance fell to the diminutive Dagenham midfielder Matt Ritchie but the youngster could not leap high enough to head in a searching Danny Foster cross in the ninth minute.
Ben Strevens came closer two minutes later when he thundered inches wide after being set up on the edge of the Luton box by Sam Saunders.
Daggers took the lead in spectacular style in the 20th minute when Foster reacted quickest to slam a scuffed Ritchie cross past Lewis Price from ten yards.
Town nearly struck back a minute later when Asa Hall saw his powerful 25-yard strike smack off the base of Tony Robert's post.
Tom Craddock blasted another good chance over the bar from close range in the 31st minute after pouncing on a loose ball in the Daggers' area.
Craddock prodded wide from point blank range five minutes later, when a deflected Ian Henderson shot cannoned back off of Robert's legs and into his path.
The forward reacted too slowly again when he found himself one-on-one with Roberts in the 50th minute only for the keeper to smother well when he delayed his shot.
Dagenham striker Jon Nurse missed a gilt-edged chance to double his side's lead two minutes later when he raced past the Town back line, only to fire straight at Price with the goal gaping.
Foster was more clinical in the 56th minute when he nipped ahead of his marker to toe-poke a superb Saunders cross past Price to double the lead for the home team.
Town hit back within a minute when Craddock teed-up Henderson with a clever lay-off. The well-placed winger drilled past Roberts and into the net from the edge of the box.
Dagenham substitute Anwar Uddin came to his side's rescue in the 85th minute when he made a last ditch challenge on Craddock as the midfielder prepared to strike from close range.
Town threw men forward in search of an equaliser but never looked like breaching the Daggers' defence.