Former England Under-19 winger Elito opened the scoring after 10 minutes with a cool finish before Chris Zebroski missed a golden opportunity to draw Newport level when he blazed over from the penalty spot.
Elito made him pay by firing in his second after 43 minutes and although Robbie Wilmott's free-kick halved Dagenham's advantage just before the break, the visitors held on to extend their unbeaten run to five games.
Daggers manager Wayne Burnett was sent to the stands at half-time for confronting referee Chris Breakspear over the timing of the free-kick, while Newport captain David Pipe was also sent off late on for a second yellow card.
Hackett said: "It was a bad time to concede a goal.
"We knew it would be a direct game given the condition of the pitch but we got our rewards early on.
"We created plenty of chances in the first half and could have been 4-0 up.
"But Medy is going through a great vein of form and has the extra class that we need right now.
"They threw the kitchen sink at us in the second half but we're proud of the way the players didn't panic and held out for the win.
"We've shown some great form in recent games, especially away from home."
- Sports & Recreation
- Chris Zebroski