The defeat compounded a miserable week for the Exiles, after striker Chris Zebroski was jailed for four years and four months on Friday.
Three goals in 11 second-half minutes from Ashley Hemmings, Christian Doige and Alex Jakubiak sent County crashing to their fourth straight reverse.
Aaron O’Connor and David Tutonda scored consolation goals, but they could not stop the Exiles slipping into ninth place in Sky Bet League Two.
The Daggers had goalkeeper Mark Cousins to thank when his spectacular save from Aaron O’Connor’s shot kept the scores level. The keeper’s fingertips then denied 16-year-old Regan Poole his first senior goal 65 minutes in.
The deadlock was finally broken after 78 minutes when Hemmings headed Wayne Burnett’s side in front. Substitute Doige then doubled the Daggers’ lead, slotting coolly past Joe Day.
Alex Jakubiak then made it 3-0 with two minutes to spare before O’Connor and Tutonda struck in stoppage time, but it was too little, too late for the hosts.