The triumph was just reward for a pulsating Blades second-half performance which was laden with controversy in a highly-charged atmosphere.
Harry Wilson’s wonderful free-kick leveller eight minutes after the break had arrived shortly after referee Geoff Eltringham turned down a huge appeal for a penalty at the other end after McGoldrick went down under pressure from Fikayo Tomori.
Tempers flared in the Derby goalmouth between both sets of players after Wilson’s equaliser- but the Blades afforded themselves the last laugh.
The hosts - who had taken the lead shortly before the break following a typically clinical Billy Sharp header - regained the lead on 64 minutes when McGoldrick was sent clear and deliciously lobbed the ball over Scott Carson.
Derby had their moments on an even first half with their best opportunity coming when George Baldock cleared an effort from Wilson off the line.
The Rams loanee fared better with his deadly equaliser, but the afternoon belonged to the Blades, who leapfrogged Derby in the table following a dominant and relentless performance for the bulk of the second period.
A sweet afternoon was crowned by Clarke’s late header, which deflected in off Jayden Bogle.
Sheffield United: Henderson; Basham, Egan, O’Connell; Baldock, Norwood, Fleck, Stevens; Duffy (Clarke 80), McGoldrick, Sharp. Substitutes unused: Coutts, Stearman, M Johnson, Moore, Cranie, Washington.
Derby County: Carson; Bogle, Keogh, Tomori, Wisdom (Waghorn 85); Huddlestone (Evans 70), Bryson, Mount; Jozefzoon (Nugent 69), Marriott, Wilson. Substitutes unused: Pearce, Roos, Holmes, Bird.
Referee: G Eltringham (Tyne and Wear).