Wednesday had survived a wealth of scares, with goalkeeper Kevin Pressman keeping them in the game for long periods.
However, with an hour gone the game opened up and both sides hit the woodwork before Owusu's opening goal.
Brought on only a minute before, Owusu was alert to a rebound as Kuqi's header rattled the bar, and with his first touch of the ball nodded into the gaping net to the delight of the Wednesday fans.
Stuart McCall had seen one shot flash narrowly wide and a second batter a post, and at the other end Paul McLaren had also had on effort flash past the near post and an acrobatic overhead hit the face of the bar.
But the match was sealed nine minutes from time when Kuqi timed his run to perfection to slam home a diving header and send Hillsborough into raptures at their first win of the season.
A hard-fought first half entertained the crowd, and it was the red half of the city that carved out the best chances.
Youngster Michael Tonge was the star of the show, but found bad fortune and the form of Pressman in the way of a derby goal.
Pressman provided the moment of the first half when he saved brilliantly low down to his left when John-Paul McGovern picked out the bottom corner with a drive.
The veteran keeper then made a follow up save from the resultant corner, and also saved well from Tonge at his near post.
Tonge then had a goal-bound shot cruelly blocked by the heel of team-mate Carl Asaba, after he had cut inside two defenders and driven towards goal.
The biggest cheer of the opening period came when referee Tony Leake was felled when a quickly taken free-kick from Asaba struck him heavily on the temple.
But it was the second period that really took on the derby air, with both sides desperate to steal victory, and United guilty of wasting several gilt-edged chances.
Asaba delayed in a one-on-one situation and fired straight at the grateful Pressman, and the spritely Tonge often chose to dribble rather than shoot when well placed.
Asaba's day was summed up when Peter Ndlovu saw Pressman save well when the substitute was put through, and the hapless striker failed to turn the rebound into the empty net.
The misses were to prove costly, and after dominating for long periods, The Blades were made to pay when The Owls finally found a route into the game, by using their heads.
The other first division fixture of the day saw Ipswich hold Preston North End to a goal-less draw.
The two sides battle hard for their respective points, but defences stood firm.
Click the links below for further match coverage:
Preston v Ipswich
Sheff Wed v Sheff Utd
