The former Brentford striker nodded home after 73 minutes to the delight of Wednesday fans, who had seen their side pegged back for long periods by the Blades. 
And United's agony was completed on 81 minutes when the lively Shefti Kuqi headed a second to seal Wednesday's first win of the season in a thrilling match.
The opening was tense, but United's Michael Tonge brought Blades fans to their feet, as he beat three Wednesday defenders before sliding the ball across the face of goal.
The Blades enjoyed more of the early possession with Wednesday not producing a shot in anger until Leon Knight's effort after 17 minutes.
Wednesday keeper Kevin Pressman had to produce two superb saves inside one minute.
First he stopped John-Paul McGovern's 12-yard shot with a sharp dive to his left, then from the resulting corner he deflected Iffy Onuora's goal-bound header, which was subsequently cleared.
Another mazy Tonge run on 33 minutes ended with a shot which forced a good save from Pressman.
Stuart McCall for United, and Kuqi for Wednesday both saw half-chances go begging, and a Tonge shot was blocked by team-mate Onuora on the stroke of half-time.
United began the second half at a pace, forcing a string of corners, and hitting the post after one goalmouth scramble.
The Blades fashioned a great chance on the hour when the tenacious McCall broke forward and fed Carl Asaba, but the striker's first touch slowed the momentum, and Pressman made another good save.
Wednesday nearly scored against the run of play on 64 minutes when Kenny spilled a high ball and Robert Ullathorne cleared Kuqi's header off the line. Seconds later, Paul McLaren fired inches wide as the home side came back.
McLaren was cursing his luck again three minutes later as he hooked the ball over his shoulder, only to see it bounce off the crossbar with Kenny beaten.
The action was intense, and United again regained the initiative with another flurry of corners which culminated in a McCall piledriver rattling Pressman's left hand post.
A goal seemed inevitable and it finally arrived on 73 minutes in typically dramatic fashion. Kuqi's looping header bounced off the post and rebounded to Owusu, who instinctively nodded the ball into the net.
Eight minutes later, Kuqi got his reward for a tireless display latching on to a brilliant cross from Alan Quinn to fire an unstoppable header past Kenny and put Wednesday 2-0 up.
In injury time, United's afternoon was summed up as Pressman produced another great save from Peter Ndlovu, only for Asaba to fire the rebound into the side netting with the goal gaping.