Jake Eyre scored a late goal to see United take all three points at Hillsborough on Friday afternoon.
United's first win of the season, after consecutive score draws, was richly deserved, although the Blades were indebted to goalkeeper George Willis, who made two timely interventions in injury-time.
The visitors started brightly in S6 with Johns marauding down the left before setting up Khan for the Blades' first attempt on goal. At the other end Willis was alert to deny to Harvey, diving away to his left.
In the 11th minute, United took a deserved lead in front of the Kop, SMITH beat the offside trap and kept his composure to finish confidently.
The advantage only lasted for seven minutes, though, as SAVIC equalised for the Owls very much against the run of play, bundling the ball home from close-range.
Surrendering the lead didn't affect United's confidence going forward though and the impressive Johns saw his rasping drive from the edge of the area go narrowly over the crossbar as half-time approached.
The second-half followed a similar pattern to the first in terms of United enjoying the lion share of possession, although goalscoring opportunities were at a premium, that was until the 88th minute when the Blades snatched the winning goal their industry deserved.
EYRE, who again was lively up front, volleyed home into the top corner, much to the delight of the Blades contingent inside Hillsborough.
The drama didn't end there, though, from the kick-off Willis made a great save scrambling across his goal and in injury-time Kedman headed off the line, before United's number one bravely claimed a free-kick in a crowded penalty area.
This was United's second win over Wednesday this season, after the U18s registered a 2-0 success at Middlewood Road earlier this month.
Chris Morgan said afterwards: "It is always nice to win a Sheffield derby, especially at Hillsborough. The boys acquitted themselves excellently and I am proud of each one of the lads.
"To have played the first three games at St Andrews, Bramall Lane and Hillsborough is very beneficial for the development of our young players."
Blades: Willis, Hodder, Kedman, Dimaio (Whiteman 71), Banton, Evans, Smith, Whitehouse, Eyre (Cockerline 89), Khan , Johns (Coustrain 62).
Unused: Owen, Scarisbrick.