After a slow opening to the match at the King Power Stadium, Nugent broke the deadlock after 21 minutes from the edge of the area.
One would become two on the stroke of the break courtesy of former Villa striker Vassell. Neil Danns was the creator, wriggling free of his marker before drilling a shot low at goal. The ball rebounded of the post, with Vassell reacting quickest to convert from close range.
The Foxes continued to dominate after the restart, but their third of the evening took until the 86th minute to arrive. German striker Schlupp was the scorer, sending a half-volley in off the woodwork from six yards out.
Further salt was rubbed into the Derby wound in stoppage time when Lloyd Dyer's low effort squirmed through the legs of goalkeeper Frank Fielding.
Nigel Clough's Derby rarely threatened Kasper Schmeichel's goal throughout the match and they end the day third in the Championship table.
Hosts Leicester have moved up to eighth.