With Danny Slatter replacing the injured Jay Saunders in midfield, the Fleet struggled to get their game going and the Daggers edged the first half hour, culminating in the opening goal on 31 minutes.
A corner from the left by Paul Bruce was met by Lee Goodwin at the far post and his firm header crossed the line despite a despairing challenge from Scott Gooding.
When it seemed like the Fleet would find Dagenham hard to break down it was left to hitman Charlie MacDonald to conjure up an equaliser.
With five minutes to go before the interval, skipper Bobby Bowry skipped through two midfield challenges before sliding the ball to Bradley Johnson on the left wing. Johnson glided a precision cross to the near post where MacDonald rose to plant a header past Roberts for his eleventh Conference goal of the season.
Sean Blackett headed on to his own crossbar on 63 minutes and a minute later Moore replaced Paul Benson and the game turned in favour of the Daggers.
With Moore's darting runs Dagenham surged forward and on 86 minutes he was left unmarked to put them ahead from a Glen Southam cross.
Moore sealed Dagenham's victory with his second four minutes later when, once again left unattended, he fired past Craig Holloway after the keeper beat out his first effort.