The Shrimps produced a fine performance to pick up an excellent point at Victoria Road.
Against a side that had won all four home games his season the Shrimps endured a torrid first half but came back strongly in the second period with a Phil Jevons penalty bringing them back into the game.
Dagenham piled on the early pressure and forced a host of early corners as Danny Green and Danny Spiller dominated the midfield.
Mark Arber headed one of those corners just over and the dangerous Josh Scott saw a low shot well saved by Barry Roche.
The Morecambe defence looked solid despite the pressure but were finally broken on 37 minutes Scott was found by Green and although his first shot was beaten down by Dave Artell the young striker superbly slotted home the rebound past Roche.
The second half began with the Shrimps looking much sharper and they were rewarded with a penalty just after the hour when Tony Roberts brought down Stewart Drummond and Jevons sent the Daggers' keeper the wrong way from the spot.
Dagenham came back strongly with Scott heading wide and Paul Benson firing inches wide of the left hand post.
Morecambe: Roche; Curtis, Bentley, Artell (rep Parrish 56), Adams, Wilson; Craney (rep Duffy 76), Drummond, Hunter, Jevons, Mullin. Subs: Davies, Moss, Stanley, Twiss, Duffy, Parrish, McStay.
Dagenham: Roberts; Doe, Arber, Antwi, Griffiths; Green, Thurgood, Spiller, Gane, Benson, Scott. Subs: Lewington, Nurse, Thomas, Ogogo, Montgomery, Bingham, Tejan-Sie.
Ref: S Cook.