Few can say that United don't entertain under Chris Wilder and the Blades deserved this victory in a highly impressive performance.
Billy Sharp twice rolled into an empty net either side of an own goal as the Blades made it three home league wins from three in the Championship.
With Clarke suspended, Lavery got the nod to start with Sharp, whilst loan capture Carter-Vickers, signed from Spurs on Friday, was on the bench.
In the S2 sunshine, United settled quicker than the visitors and won a corner and a couple of throws in the opposition's half before being gifted the lead on four minutes. The experienced Carson fluffed his clearance from the left of his goal and SHARP coolly slotted into the unguarded net with a first time effort from 20 yards.
The visitors looked for an instant response but Vydra was held up by Wright and O'Connell stole the ball, whilst in a hectic opening half hour the Blades were more positive. Coutts shot wide after a good build up.
On the break Derby looked a threat, no more so than on 36 minutes when Vydra raced clear but Fleck tracked him all the way into the penalty area and timed his tackle to perfection.
Russell was the next to go close, curling over following another break but the winger's next contribution was more defining on 39 minutes. Duffy, Freeman and Lavery linked up and to prevent the latter getting a shot in, RUSSELL's attempted clearance could only find the bottom corner of his own net.
Derby had a couple of opportunities to reduce the arrears before the break, including a cheap free-kick, but United held firm and deserved their applause at the half-time whistle.
It was the visitors who made the better start to the second period but Huddlestone was off target and Blackman saved from Vydra. An accidental clash of heads between Olsson and Lavery saw both players return to their feet but the Blades striker was replaced by Evans.
Derby made a double change before the hour and Carruthers replaced Duffy in a fractious spell of free-kicks conceded by both teams, although the referee ignored Vydra's appeals for a penalty on 65 minutes.
United went close when Carruthers drilled a cross along the six-yard box and O'Connell was penalised for climbing at the back post as the home side threatened again.
Carruthers picked up a knock and was replaced by Lundstram for the final 10 minutes. Late on Johnson headed Wisdom's cross wide and a speculative Lawrence shot caused a problem for Blackman but the ball flew wide of the post.
On 85 minutes, United went close when Sharp latched onto a Stevens through ball but Carson made an impressive one-handed save and Freeman took on a few Derby defenders in the penalty area.
As seven minutes of injury-time approached Martin headed wide a Lawrence cross but the visitors did score to cause a few nervous moments. A Johnson cross saw BRYSON arrive late in the box to head home.
Derby, expectedly, threw caution to the wind, but left holes at the back. Sharp had the ball in the net but he was offside as he received Lundstram's pass and the skipper then turned provider to put Fleck in but Carson blocked.
Carson's next contribution was to head into the Blades box for a very late free-kick and he was left stranded as the Blades broke away and SHARP kept his coolly to roll into the unguarded net - again - to confirm the victory.
Blades: Blackman, Stevens, Fleck, O'Connell, Basham, Sharp, Wright, Coutts, Freeman, Duffy (Carruthers 64, Lundstram 81), Lavery (Evans 54).
Unused: Carter-Vickers, Lafferty, Eastwood, Brooks.
Derby: Carson, Keogh, Russell (Lawrence 57), Wisdom, Johnson, Weimann (Bryson 71), Vydra, Nugent (Martin 57), Olsson, Davies, Huddlestone.
Unused: Baird, Pearce, Butterfield, Mitchell.