John Still's men took the game to their hosts from the off and thoroughly deserved their win against the play-off hopefuls.
Glen Southam and Chris Moore grabbed two goals apiece as Woking rued the absence of key men Gary MacDonald, Ian Selley and Jon Boardman.
Moore lobbed the first after Luke Oliver had made a hash of clearing a long Tony Roberts kick.
And although Jefferson Louis equalised with a good turn and shot, Daggers restored their lead when Southam side-footed home after a great run and centre from Craig Mackail-Smith.
With Moore floating an effort wide just after the break, a scintillating 25-yard volley from Paul Bruce smashed the underside of Woking's crossbar.
It was a magical moment which seemed to inspire Southam. The right-sided midfielder easily beat Liam Cockerill on the right before lashing a superb strike which beat Shwan Jalal for shear pace to make it 3-1.
Mackail-Smith's free header from six yards might have made it four as Woking struggled going forward with leading scorer Justin Richards on the bench.
The Cards were lucky not to go 4-1 down when Moore's breaking run set up Southam but he scuffed his hat-trick chance, hitting the inside of the post when he seemed certain to score.
It didn't matter though as despite being under the cosh for a spell when Amos Foyewa and Richards had come on to liven things up, Moore nutmegged Jalal for the fourth before Richards notched a consolation.