The Rams face a real battle ahead if they are to avoid the drop and they showed the right spirit to clam the points over The Gills.
Jamie Vincent was signed from Portsmouth on Friday and he marked his debut in perfect fashion with the opening goal.
Vincent staked his claim for hero status at Pride Park with a superb free-kick on 12 minutes.
Gillingham's hopes of getting back into the game were dealt a blow when John Hills saw red on 28 minutes.
Derby extended their lead on the hour when Rob Edwards, on loan at the club from Aston Villa, smashed home from 30 yards.
Tommy Johnson scored a belter of his own 20 minutes from time to give Gillingham hope, but they were reduced to nine men when Ian Cox picked up two bookings in as many minutes and his exit ended the visitors' hopes of snatching a point.
