Billy Sharp turned in United's late winner in an action-packed encounter with second-placed Coventry City.
United weathered a storm before substitute Sharp earned the Blades three welcome points.
Manager Adkins made three changes for the televised clash with the Sky Blues, playing in red! Edgar, Woolford and Sammon all started, Harris missed out through injury, Adams was suspended and Sharp dropped to the bench.
Coventry made United kick towards the Kop in the first half but not before moving tributes to former Blades goalkeeper Alan Hodgkinson MBE and Official Club Photographer Martyn Harrison, who both passed away earlier in the week.
There was an element of sizing each other up in the opening 15 minutes and neither side could claim to be on top. The first chance arrived on 19 minutes when Lameiras provided a ball through the defence for Armstrong and whilst United appealed for offside, Long made a tremendous save.
The goal gave Coventry impetus and McEveley was booked for a late challenge on Lameiras. Turner missed twice from the same corner.
A couple of Blades corners caused problems for the Coventry defence, although Charles-Cook always looked keen to come off his line. Late in the half Hammond was booked for an accumulation for fouls and the visiting side's Turner was also cautioned for a cynical challenge on Done.
Close to the break United wasted a couple of chances to test Charles-Cook before the half-time whistle left all to play for in the second half.
The early opportunities in the second period came from the visitors. Fleck's long-range strike was wide and then Long produced another fine save to keep out Lameiras after an attempted Collins clearance dropped to the Coventry player.
On 63 minutes Coventry went tremendously close. Armstrong robbed Collins and from his low cross, Fleck and Murphy failed to attach themselves to the ball with the goal gaping. Soon after they went closer still! Murphy beat Brayford and from his cross there were a number of ricochets ahead of Long dropping on the ball with the Coventry players appealing that it had crossed the line.
Between the aforementioned chances, Sharp was introduced for United and the next chance - the first of the half for the Blades - was to be crucial.
On 80 minutes Coutts delivered a corner from the left and after Charles-Cook failed to gather in a crowded box, SHARP managed to turn the ball home, although it took an age to cross the line! The Sheffield-born striker celebrated by kissing his black armband.
Predictably, the Blades slowed the action in the final ten minutes and professionally protected Long. Coventry got more desperate late on and Ricketts was sent off for a second bookable offence in five minutes of injury-time.
Late on Flynn, on as a substitute, used up valuable seconds and forced a save out Charles-Cook, whilst the Blades were on the offensive as the referee's final whistle signalled three vital points.
Blades: Long, Brayford, Basham, Coutts, Done (Flynn 84), Collins, Woolford (Scougall 54), Sammon (Sharp 65), McEveley, Edgar, Hammond.
Unused: Howard, Reed, K Wallace, McGahey.
Coventry: Charles-Cook, Stokes, Vincelot (Antoine-Fortune 81), Fleck, Lameiras (Kent 70), Armstrong, O'Brien (Cole 60), Turner, Ricketts, Martin, Murphy.
Unused: Burge, Tudgay, Haynes, Kelly-Evans.