Luke Howell and Dwight Gayle helped themselves to a brace apiece as the hosts outplayed and outfought their visitors.
Dagenham took the lead after five minutes when they caught the visiting defence napping and Jake Reed's cut-back from the byline was thrashed in by Dwight Gayle.
Millers loanee Lee Frecklington had a volley superbly saved at the other end but they were second best all over the park and could have no complaints when the home side doubled their lead in the 35th minute.
Left-back Oluwafemi Ilesanmi skinned debutant Luke Rooney on a charge from inside his own half and cued up Luke Howell to pick his spot from 20 yards.
Dagenham maintained their stranglehold in the second half and Andy Warrington kept Rotherham in the contest with two great saves before Howell turned in his second from another Ilesanmi feed to make it 3-0 with 15 minutes to play. Medy Elito drilled in their fourth goal nine minutes from time and Gayle's injury-time header completed Rotherham's misery.
