Diego De Girolamo netted a first-half brace to pave the way for a deserved success over Coventry City at the Alan Higgs Centre on Monday afternoon.
The victory sees United's youngsters extend their current unbeaten in the Professional Development League to 13 matches and in the process complete a double over the Sky Blues.
On a bright afternoon in the Midlands, it was the home side who started on the front foot with Kelly-Evans and Stevenson both having efforts on goal, with the latter forcing Ramsdale into a save.
But it was the Blades who drew first blood in the 20th minute as DE GIROLAMO swivelled to open the scoring, firing into the bottom right-hand corner from 18 yards out.
That goal saw the Blades stamp their authority on the game and Wright could have made it two in the very next attack, but on the half hour the visitors did double their advantage and it that man DE GIROLAMO who reacted quickest in the box to score from close-range.
On the stroke of half-time, City wasted a golden opportunity to reduce the arrears, as George Thomas found himself clean through on goal, but Ramsdale was out quickly to smoother the danger.
The home side were again out of the traps quickly in the second period and just before the hour STEVENSON capitalised on a defensive error to give the home side a lifeline.
But the final 30 minutes saw little in the way of goalmouth in the visitors box as United's defence stood firm to ensure a fourth win of 2016 and in doing so keep pressure on league leaders Huddersfield Town.
Blades: Ramsdale, Gordon, Kelly, Gilmour, Kennedy, Semple, McFadzean (Hall 87), Whiteman, Wright, De Girolamo (K. Smith 78), Brooks.
Unused: Adebowale, Eastwood, Hallam.