Spireites striker Jamie Ward was in superb form, netting either side of half-time, before midfielder Steve Fletcher scored the third with a bullet header late in the second half.
Chesterfield came close to breaking the deadlock in the sixth minute, when midfielder Jamie Lowry outwitted Daggers skipper Anwar Uddin before seeing his audacious lob drop inches wide of Tony Roberts' goal.
The visitors upped the pressure, with midfielder David Dowson outpacing Daggers full-back Scott Griffiths in the 20th minute, before firing a vicious strike narrowly wide from 25 yards.
Former Wales international Roberts was finally beaten in the 36th minute, when Ward saw his powerful strike deflected into the net off of Daggers defender Ross Smith.
Daggers poured men forward in search of an equaliser, with midfielder Glen Southam thundering in a powerful close-range strike in the 40th minute which Barry Roche did well to block.
The Spireites caught Daggers with a sucker punch 50 seconds into the second half, when Ward lost Uddin on the edge of the box before calmly slotting past Roberts for his second goal of the match.
Dagenham nearly struck back immediately, with substitute Sam Sloma firing straight at Roche from six yards after connecting with a searching cross from Shane Huke.
Daggers striker Jon Nurse should have pulled one back in the 63rd minute, but fluffed his shot after slipping on the ball with the goal at his mercy.
Paul Benson missed another golden opportunity for the home side in the 72nd minute, when he raced clear of the Chesterfield back line before pulling his shot wide of target when one-on-one with Roche.
Fletcher finally sunk Daggers in the 78th minute, when he out-jumped Uddin to power a bullet header over Roberts and into the back of the net from ten yards.
The home side threw caution to the wind in search of a late consolation goal, but never looked like troubling Roche.