Derby were not without their chances, though, with a 20-yard strike from Hughes testing the palms of Ben Foster late in the half.
West Brom had the lead in the latter stages of the first period, however, when Dorrans thumped a long-range drive into the bottom corner.
Anelka came close to adding West Brom's second in the opening minutes of the second half, but his curling effort went straight into the arms of Lee Grant.
Jonas Olsson and Long also had opportunities for the Baggies as the half began to gather pace, but neither could find their second. The tempo dropped in the latter stages as both managers made changes.
Morrison might have added West Brom's second after 86 minutes, but his long-range effort was denied by Grant.
The Baggies did double their tally in the final minute, however, when Markus Rosenberg turned home from close range.