Recent defeats for the Daggers have all but dashed their hopes of a play-off place, but this victory will no doubt boost confidence for John Still's young side.
It was Morecambe striker Danny Carlton who seemed intent on winning the game for his side early on, as he had a number of opportunities to open the scoring during a goalless first half.
Carlton's best chance came early on. Through on goal, the striker was thwarted by a terrific low save by Tony Roberts.
Arguably the best chance of the first half came at the other end. The industrious Craig Mackail-Smith worked tirelessly in winning possession before finding Cliff Akurang. Steven Drench blocked Akurang's attempt, while Glen Southam's follow-up was deflected over.
All four goals came in the second half and it was the home side who found the back of the net first. Just a minute had passed in the second period before Mackail-Smith scored from close range.
It was due reward for the Daggers striker, who was rightfully named man of the match by the home sponsors.
The Daggers lead barely lasted a couple of minutes. The visitors forced an equaliser through Garry Thompson; his shot from the edge of the area left Roberts standing, helpless to prevent the ball from ending up in the bottom corner.
It was game on after that and Carlton continued his personal battle with Roberts. The former Wales international goalkeeper produced a superb finger-tip save to thwart a header from Carlton.
It was Dagenham who were to score next. Scott Griffiths was the creator; the full-back hit a low cross that found Southam in the penalty area. Southam hit a left-footed shot that found the roof of Drench's goal.
The game was settled after 71 minutes. Mackail-Smith was again involved.
A fantastic pass released his strike partner Akurang, who lifted the ball over the onrushing Drench to secure all three points for his side.