An 11th minute goal from Tom Horton split the difference as Newport claimed a league double over their Black Country rivals to end the season on a high.
Darlo created a number of chances to drawn level with Sam Melia twice going close but Dudley proved difficult to beat.
Newport lost the services of Shane Thomas on 71 minutes for a crazy two footed tackle on substitute Allen, but despite this Darlo were unable to find that all important finishing touch despite having much of the play second half.