The Owls have now gone 14 games without a win and were fortunate to not suffer a heavier defeat on Monday.
Derby have moved up to 12th in the table, with just their second win in six games, and are now four points outside the top six.
The visitors took time to assert their dominance but pounced as Wednesday tried to play out from the back.
Thompson intercepted a loose pass and poked the ball to Bobby Clark, who found Agyemang inside the box.
With a clever shift of his weight, the striker created space outside Dom Iorfa and fired a low shot across the goalkeeper and into the bottom-right corner.
Clark almost made it two but Wednesday captain Barry Bannan bravely headed away Ben Brereton Diaz’s cross.
Another chance soon followed as the hosts were again caught in possession deep in their own half but Clark fired well over the bar from the edge of the area.
