The Rams scored three excellent goals but in between the football was typical of a game between two local teams and the result leaves Forest deep in relegation trouble.
This was a big occasion for Joe Kinnear's side but they failed to rise above what was for long periods a mediocre match.
Forest had few good moments in the game and only a penalty miss by Derby skipper Ian Taylor saved them from what could have been an embarrassing defeat.
Few of the Forest team did themselves justice and the visiting fans poured their frustration on Kinnear when he replaced David Johnson with 17 minutes left.
Just as in the corresponding fixture last season, Derby began well and went in front in the fourth minute. Excellent play by Morten Bisgaard on the right led to Inigo Idiakez setting up Tommy Smith who finished clinically from 15 yards.
Derby should have gone further ahead when Andy Impey used his hand to block a Taylor header.
Impey was booked - the first of nine yellow cards in the game - but Taylor blazed the spot kick high over the bar.
The match descended into a scrappy affair with both sides conceding possession and Forest suffered another setback when Jack Lester was stretchered off with what appeared to be a serious leg injury in the 48th minute.
Forest's best moment came on the hour when Gareth Taylor flicked on a free-kick and Johnson struck a volley from a tight angle that Lee Camp did well to keep out.
But another neat move by Derby ended with Rasiak heading Smith's cross in at the back post in the 75th minute.
Forest's misery was complete a minute form the end when Bisgaard drove in a low cross form the right and Rasiak scored from close range.