As part of Sky TV's 10in10 promotion, it was United's number 10 who stole the show.
Billy Sharp scored both goals, taking his tally to 14 for the season, on an eventful night at Coventry City's Ricoh Arena.
Chief Wilder named an unchanged starting XI for the televised encounter, although there was an enforced change on the substitutes' bench where Whiteman replaced Scougall, who was suffering with a tight hamstring.
The opening 15 minutes were uneventful - on the pitch at least - although the Coventry fans were vocal in protests against their Board. The Blades won the first corner and a routine between Coutts and Duffy put the home side on the back foot.
It appeared that the commotion off the field was prevented any cohesion on it, from both sides. It took until 22 minutes for a chance - McCann's effort was blocked but a matter of 60 seconds later the Blades were ahead.
Coventry struggled to clear and from a throw, Lafferty's cross was only partially cleared and SHARP fired under goalkeeper Charles-Cook from 10 yards.
As half-time approached, Coventry had a spell of pressure. Agyei looked a threat, but the only chance of note arrived on 42 minutes when Wright half-volleyed over following a cross from McCann.
There was an early chance for United in the second half but Done could not connect with Lafferty's teasing cross and Coventry's start after the break was rewarded with an equalising goal.
On 51 minutes, AGYEI's shot from the corner of the 18-yard box took a telling deflection off Coutts and looped over Moore's head into the goal.
A mix-up between Ebanks-Landell and Moore caused a nervous moment and the Blades goalkeeper saved comfortably from a Sordell shot on 64 minutes. United were surrendering possession far easier than in previous games and Sordell went close again following a break.
Twice in the space of four minutes, however, United went very close, and both from the same route. Lafferty, Sharp and Fleck combined for Lavery to curl a shot which shaved the outside of Charles-Cook's left post and then the same Blade struck the same post on 76 minutes; this time the ball staying in play.
Clarke was introduced as United switched to 4-4-2 and two chances in quick succession forced Coventry back. Basham's shot was blocked by Sordell and Fleck was allowed to progress to the box but Charles-Cook saved.
The Blades were now in the ascendency and Duffy forced Charles-Cook into another save before the home fans invaded the pitch, halting United's rhythm.
The teams left the field but within two minutes of the restart United were back ahead. Freeman's cross from the right saw Lavery head down and SHARP beat the home goalkeeper at the second attempt.
Time remaining was unclear due to the stoppage but United professionally saw out the closing minutes with Moore commanding his area to ensure a third successive TV win for the Blades.
Coventry: Charles-Cook, Willis, Turnbull, Bigirimana, Rose, Agyei (Thomas 68), McCann, Page, Sordell, Wright (Lameiras 74), Kelly-Evans.
Unused: Jones, Reid, Gadzhev, Tudgay, Addai.
Blades: Moore, Fleck, O'Connell, Basham, Sharp, Done (Lavery 63), Coutts (Clarke 75), Freeman, Ebanks-Landell, Duffy (Whiteman 90), Lafferty.
Unused: Hussey, Ramsdale, Wright, Brown.