United States striker Agyemang struck in each half, either side of Liam Thompson's effort early in the second period, as Derby halted a three-game winless run to climb up to 12th in the table, four points adrift of the playoffs.
Derby manager John Eustace said Agyemang, who took his goals tally for Derby to five since signing from MLS side Charlotte FC for £7.3 million ($9.75 million) in July, was disappointed not to have scored a hat trick after being denied by Owls goalkeeper Pierce Charles' excellent late save.
"He actually said to me, 'I should have got the third.' You know, he was disappointed," Eustace said after the match. "But I'm delighted. The more goals he gets, obviously the better. The first finish was excellent. I didn't think he was playing particularly well before that.
"But that finish for his first goal was a top finish and I'm so pleased for him to get the second. He still had to put it away. It's a good poacher's goal. His performances are getting stronger."
The beleaguered Owls' wait for a first home league victory of the season continues, while their winless run was extended to 14 matches.
After being docked 12 points in October for going into administration -- with a further six points deducted earlier this month for other financial breaches -- Wednesday remain a club in turmoil.
Their shortcomings on the pitch were all too apparent as their fans wait to learn which of the 12 parties interested in a club takeover has been granted exclusivity by the administrators.
The first half was devoid of any quality as both sides repeatedly gave away possession, with home and away fans' patience tested.
That was until the 32nd minute when Derby broke the deadlock with their first real chance of the match.
Rams midfielder Bobby Clark slipped in Agyemang on the left edge of the box, having pounced on another misplaced Owls pass out of defence, and the latter all too easily bypassed Dominic Iorfa before drilling a low finish into the far corner.
Derby gained full control before halftime as Ben Brereton Diaz's shot from the edge of the box was well saved by Charles and Clark wasted a chance as he blazed over.
A tussle between Agyemang and Iorfa early in the second half sparked a brief mass melee, which resulted in bookings for both players, before Derby doubled their lead.
Craig Forsyth's free kick fell to Thompson just inside the area and his low finish bounced inside Charles' left-hand post in the 57th minute.
Derby put the game to bed five minutes later when Agyemang slammed home his second from eight yards following Rhian Brewster's square pass and what little confidence Wednesday had left all but evaporated.
Agyemang was denied his hat trick by Charles' excellent low save and Derby substitute Kayden Jackson was also thwarted by the Owls goalkeeper as the visitors looked to increase their lead.
Information from PA was used in this report.
