The Daggers gave ill boss John Still the perfect fillip with victory over the side that joined them in the Football League from the Conference in 2007.
Still didn't travel to the game because of illness but stand-in boss Terry Harris will be able to give the boss the perfect tonic with the report of his side's third win in four games.
The visitors won the game with two goals in quick succession at the start of the second half.
On 50 minutes home defender Henry McStay gave away a silly free-kick on the right edge of the box with a clumsy challenge and Sam Saunders made him pay with a curling effort that beat the flat-footed Barry Roche at his near post.
And the Daggers really stuck the knife in Morecambe's hopes when just a few minutes later Michael Carr gave the ball away sloppily in midfield and was made to pay.
Scott Griffiths' run into the box ended with a Paul Benson shot that was blocked only for Solomon Taiwo to lash the loose ball into the top of the net to make it 2-0.
After Garry Hunter and Stewart Drummond were brought on in midfield for the Shrimps the home side upped the tempo considerably and made a couple of chances with Neil Wainwright putting in crosses from the right.
Drummond was inches away from connecting with one and then Matty Blinkhorn volleyed horribly high from close range from another.
But the final substitution did bring its rewards for the Shrimps. Former Celtic youngster Diarmuid O'Carroll came off the bench and with his first touch headed home a Wayne Curtis flick-on with 11 minutes to go to give his side hope.
O'Carroll then had a chance to equalise after Rene Howe broke superbly down the left before cutting a pass back to the striker but his shot was blocked and his second effort flew over leaving Dagenham with the three points.
The first half saw plenty of effort with few clear chances although Jim Bentley and Ben Strevens both should have done better with good opportunities at either end of the field.