Lucas Joao's double gave the Owls their first league win under manager Jos Luhukay and lifted them nine points above the relegation zone.
Derby, who suffered a Championship defeat for the first time since November, dominated the ball but were undone by a clinical home side, who took the lead when Lucas Joao fired in Jack Hunt's layoff after 18 minutes.
The Portuguese forward secured the win two minutes after the break, cutting in from the left before rifling past Scott Carson.
The defeat means Derby stay third in the table, a point behind second-place Aston Villa, having played a game more.
Cardiff City was able to move level with the Rams on 58 points, meanwhile, as they saw off Bolton Wanderers 2-0 in Wales.
Armand Traore's first goal for the club put them ahead 34 minutes in before Sean Morrison nodded home the second just before the break at Cardiff City Stadium.
Bolton offered little threat of a comeback in the second half and remain just two points outside the bottom three.