The Daggers 100% record at the London Borough of Barking and Dagenham came to an end as they were held to a point by a physical and highly organised Morecambe side.
The home side had to play in their yellow kit after Morecambe's first and second choice strips both clashed with the Daggers home jersey.
Danny Spiller came in to make his first start for Dagenham and Redbridge and the midfielder seemed keen to make an impact. Early on he combined with Danny Green before flashing a shot across goal that was cleared.
That effort apart, the Daggers struggled to get going in the early stages and it seemed to take a while to get their defensive line sorted. They were almost punished after Stuart Thurgood's loose ball made its way to Phil Jevons. The loanee burst clear on the left but his cross was fielded by Tony Roberts.
Set-pieces appeared the most likely source of a goal for the Daggers. They forced a flurry of corners during the first half, one of which saw Mark Arber head over the bar.
Slowly the Daggers became more of a threat. Josh Scott drove across goal while Paul Benson saw a header go several yards wide of goal.
Morecambe's best moment came halfway through the first half. Jevons rolled in his strike partner Paul Mullin, but the former Accrington man was denied by a super tackle from Scott Doe.
Doe and Green were enjoying plenty of the ball on the Daggers right. Green set up Griffiths who blasted over while another cross from the winger saw Benson nearly repeat his goal of last week, only this time Barry Roche was on hand to make the save.
Scott saw another shot blocked by David Artell before the Daggers industry was finally rewarded with the opening goal on 37 minutes.
Benson conjured up a fine pass that allowed Scott to hit a first time shot. That effort was stopped by Artell but Scott was on hand to recover the loose ball before planting it into the bottom corner.
The half finished with Spiller having another crack from distance. On this occasion the ball flew wide of the post.
The Daggers survived an almighty scare soon after the restart. Laurence Wilson shot past Roberts and the ball somehow missed Ian Craney in the centre of goal before Griffiths rescued his side with a flick off his own goal-line.
Morecambe certainly started the second half the better. Doe had to block an effort from Wayne Curtis while Roberts just did enough to prevent Mullin from getting to the loose ball.
Griffiths was involved at the other end; reacting quickest after his drilled cross was blocked, but his right footed effort was weak and easily gathered by Roche.
Just as when John Still thought his side might have weathered the Morecambe pressure, the visitors forced an equaliser. It came from the penalty spot after Stewart Drummond was tripped in the area by Roberts. Jevons took the kick and duly sent Roberts the wrong way.
The manager would have been satisfied with Dagenham's response to the equaliser; a winning goal pretty much the only thing missing.
That wasn't for lack of attempts. Both Scott and Arber had headers while Peter Gain saw shot punched away by Roche.
Scott meanwhile held off sub Andy Parrish before turning and aiming a shot at the far post. The ball just didn't curl enough and narrowly missed the goal. Green also embarked on a run directly at the Morecambe defence which ended in a shot that flew just wide.
Morecambe's chance to claim all three points fell to another, Mark Duffy turned and hit an effort that Roberts just about gathered. The keeper needed a couple of goes at claiming the ball.
The Daggers final chances fell to Benson. He turned and shot wide after latching onto to a long throw before being denied by Roche when faced with just the keeper to beat. That was the game's final attack and the Daggers were made to settle for a draw.
Att: 1,770 (73 Morecambe)