Yet another home defeat to yet another late, late goal means the Daggers form is now a serious cause for concern.
The Daggers got a flying start with a goal from Billy Bingham
after only five minutes. But they failed to build on it.
Things looked good for them when Shrewsbury had defender Jermaine Grandison sent off in the 48th minute for a foul on Ade Yusuff.
But the Shews made nonsense of that handicap by taking complete control of the game.
They were so superior it looked as though the Daggers were the team with a man short.
The Shrews ran the show to such an extent that Daggers keeper Mark Cousins
was forced into a string of superb saves that deservedy won him the Man of the Match award.
Shrewsbury introduced Andrew Mangan as a second half sub and he played a big part in their victory.
He scored their first goal with a magnificent volley in the 69th minute, latching on to a long through ball and lashing in a shot that gave Cousins no chance.
And with the game deep in injury time Mangan was brought down in the area and skipper Liam Lawrence slotted hom the 95th minute penalty that won the game for the visitors and left the Daggers with plenty to think about.
Dagenham & Redbridge
: Cousins, Batt, Doe, Saah, Green, Boucaud (Partridge 60), Bingham, Labadie, Porter, Cureton (Chambers 70), Yusuff (Murphy 75).
: O’Brien, Connors, Goldberg, Hemmings.
: 1,698 (299 away)