Hossam Ghaly played full 90 minutes for Derby, but the on-loan Egypt midfielder was unable to prevent the Rams from receiving their fifth straight defeat.

Derby were 1-0 up with only four minutes played, when Lewin Nyatanga hit an empty net on the rebound, but Benjani scored two goals in four minutes to put Pompey in front before half-time.

The Zimbabwe striker completed his hat-trick ten minutes into the second half with a slick finish, scoring his 12th of the season.

Derby, who are without a win since September 2007, remain bottom with seven points, while Portsmouth are eighth with 37.