United deserved at least a point from the first Sky Bet Championship encounter of 2018.
Leading scorer Leon Clarke netted the equaliser after Matej Vydra opened the scoring with a penalty. 3,109 Blades fans made the trip and watched a mighty effort.
Wilder made two changes, Baldock and Donaldson were handed starts with Carter-Vickers and Sharp dropping to the bench, meaning another change of role for Basham.
The first attempt saw Clarke's effort deflected wide by Keogh and the Derby man's central defensive partner, Davies, turned the ball into his own side-netting following Basham's low cross.
Derby's first attempt saw the ball drop nicely for Vydra but he blasted over and United had made the brighter start, winning a number of corners.
However, the home side were handed the lead on 24 minutes. Russell harassed Baldock, who was trying to shepherd the ball out of play but was forced to handle to prevent the Derby player getting free. Referee Bond awarded a penalty and VYDRA blasted past Moore.
Russell and Vydra linked up again but the goalscorer was off target and United were more than a match for the home side. On 39 minutes a great run from Donaldson caused problems for Keogh and after cutting inside, the Blades striker forced a save out of Carson.
The final chance of the first half fell to the visitors following a rapid break from a Blades corner but Weimann, on the left, flashed his shot across Moore's goal.
United began the second half with a number of deliveries into the Derby box and followed those up with a great move from right to left, which started with Donaldson holding up possession. Clarke, Duffy and Stevens were all involved before Fleck sidefooted wide.
There was another Fleck chance, which was blocked, before United deservedly levelled on 57 minutes. Donaldson found space to swing in a cross from the right and CLARKE was left free to position a header into the bottom corner, beyond Carson.
The goal and United's front-foot approached had the Derby fans nervous but despite being on top, the visitors were unable to test Carson further. Carruthers replaced Duffy, who picked up a knock, whilst Fleck's drilled free-kick was on target and deflected but comfortable for the home goalkeeper.
As the final ten minutes approached Nugent had the ball in the Blades net but Keogh fouled Clarke in the build-up and that proved to be the home side's final chance.
Derby were happy to operate on the break in an entertaining final period as United maintained the energetic performance, looking for a victory.
However, there was little to report late on in terms of goalscoring opportunities and all was left was for the fans to take the applause of the sold out away contingent after the final whistle.
Derby: Carson, Forsyth, Keogh, Russell, Baird, Johnson (Thorne 70), Weimann, Vydra (Winnall 70), Nugent (Martin 81), Davies, Huddlestone.
Subs: Wisdom, Pearce, Bennett, Mitchell.
Blades: Moore, Baldock, Stevens, Fleck, O'Connell, Basham, Lundstram (Lafferty 90), Clarke, Donaldson, Stearman, Duffy (Carruthers 77).
Subs: Sharp, Wright, Carter-Vickers, Lavery, Blackman.