The Daggers took the lead after just 18 seconds when striker Ben Strevens ran on to a clever Paul Benson lay off before clipping the ball past onrushing keeper Alan Julian from ten yards.
Gillingham were stunned, and put little pressure on the home side before winger Albert Jarrett stung Tony Roberts' palms with a powerful 20-yard strike in the 15th minute.
The Gills thought they had equalised in the 27th minute when Adam Miller rose highest in the Daggers area to head a deep cross past Roberts, only for the linesman to raise his flag for offside.
Solomon Taiwo should have doubled Dagenham's lead in the 38th minute when he pounced on a loose ball on the edge of the Gillingham box, only to pull his shot wide with the goal at his mercy.
Gills midfielder Andy Barcham should have done better on the stroke of half-time when he blasted high over the bar from 20 yards after racing on to a clever lay-off from Curtis Weston.
Daggers made an explosive start to the second half with Strevens collecting the ball 30 yards from goal in the 49th minute and sprayed a quick pass wide to Benson who blasted a powerful first-time strike past Julian and in off the post.
Benson hit the net again in the 62nd minute when he bundled a header past Julian from a Strevens cross, only for the linesman to raise his flag again after the ball was adjudged to have gone out of play.
Taiwo tried his luck from long range ten minutes from time when he thundered a powerful free-kick straight at Julian from 30 yards out.
Benson should have made it three in the 87th minute when he outpaced the Gills defence, but could only drill his shot into the sidenetting under pressure from Simon King.