Clinical finishing from Dagenham & Redbridge saw Hampton & Richmond's FA Cup dream end at the Beveree Stadium.
The Blue Square South team dominated most of the game but Aaron Barnett headed over and Tony Roberts superbly kept out Orlando Jeffrey's strike.
After the restart Godfrey's volley was turned away by Roberts, while Barrie Matthew's header flew just over.
But Paul Benson fired home before Shane Huke's stunning shot and Ben Strevens' simple finish sealed the Daggers' win.
Hampton & Richmond: Lovett, Harper (Mcauley 71), Ryan Lake (Paris 71), Jeffrey, Barnett, Wells, Inns, Godfrey, Hodges, Frost (Harris 85), Matthews.
Subs Not Used: Fernandes, Quarm.
Booked: Ryan Lake.
Dag & Red: Roberts, Sloma (Uddin 67), Boardman, Huke, Southam, Rainford, Griffiths, Benson, Foster , Smith (Strevens 66), Moore.
Subs Not Used: Thompson, Taylor, Green.
Goals: Benson 68, Huke 83, Strevens 90.
Ref: Dean Whitestone (Northamptonshire).