Ben Wright scored the only goal of the game as Braintree saw off struggling Newport, who stay in the relegation zone having not won in seven games.
Wright netted his third goal of the season after 20 minutes when he put a right-footed shot into the bottom-left corner from a Jai Reason free-kick.
Adam Bailey could have made it 2-0 before the break but fired over.
Chibuzor Chilaka and Wright again went close as Braintree continued to dominate in the second half.
VIEWS FROM THE DRESSING ROOM
Newport County manager Anthony Hudson told BBC Radio Wales:
"We got a very strong performance. They gave everything they had and that was the response we were looking for.
"We're just looking for a little break at the moment but unfortunately we didn't get it today.
"We started the game very well and a defensive mistake has cost us in the end."
Braintree Town boss Alan Devonshire told BBC Radio Essex:
"The midfield protected [us] well when we didn't have the ball - we worked as a unit.
"It's a team ethic and long may that continue. I'm delighted with the way it is going at the moment.
"It was quite physical today and the pitch wasn't the best - it was tough, and it will be tough again on Tuesday [against Hayes]."