Two of United's smallest players won headers to secure the winning goal in Saturday's home fixture with Swindon Town.
Midway through the second half a nod from Ryan Flynn set up Jose Baxter to score the all-important goal with a looping header.
The Blades gave a solid performance in the last home fixture before Christmas to move further away from the League One relegation zone.
Chief Clough made three changes to the Blades team - McMahon, White and Murphy all started, Hill and Lappin dropped to the bench, whilst McGinn failed to shake off the knock he suffered in the first half at Cambridge.
The management reverted to the favoured 4-4-2 system with McMahon and White in the full-back roles and Flynn and Murphy ahead of them, Coady was Doyle's partner in central midfield.
United dominated the first 15 minutes in terms of possession and created two good chances, despite Swindon looking well-organised defensively. A long-range effort from McMahon struck the arms of goalkeeper Foderingham and then a 20-yard free-kick from Baxter, after he was fouled, looked on target before it was deflected away by Hall.
A number of bizarre referring decisions baffled the players and supporters of both club, preventing the game from flowing as half-time approached. United failed to benefit from a couple of corners and Swindon's first effort was a blast from Ajose but Long parried away on 38 minutes.
Late in the half the Blades almost caused their own downfall. After Baxter gave possession away, Long was forced to save from Mason and moments later, in injury-time, it was the goalkeeper who failed to connect with a pass, inviting pressure, from which Doyle needed to foul Mason and collect a booking. The resulting free-kick saw Pritchard's effort blocked and then Hall hooked a corner onto the roof of the net.
The Blades began the second half well and came close to opening the scoring on 51 minutes. Doyle robbed Kasim but Baxter's shot was parried by Foderingham and Flynn's follow up was deflected wide. From the resulting corner, Baxter's inswinger to the back post saw an under-pressure Porter force the ball against a post.
From a Murphy cross, Hall deflected wide to prevent Porter getting a shot in and then goalkeeper Foderingham was penalised for timewasting, although United's free-kick was squandered.
However, the Blades were soon ahead. Midway through the second half White's cross was met at the back post by Flynn and BAXTER cleverly looped his header over Foderingham and into the Kop goal.
It was now United's time to slow down the play and Clough introduced both Brandy and Hill to the left side, whilst McMahon was booked for a foul on Mason.
Coady fired over as the game entered the final ten minutes and soon after Miller replaced the hard-working but tiring Porter.
Swindon's first effort of the second half was a long-range effort from Luongo, which did not trouble Long, whilst a tame shot from Pritchard, moments later, was comfortable for the goalkeeper.
Four minutes of added time saw the Blades attempt to keep possession, winding down the clock, whilst Swindon's Byrne was booked for a dive in the box. Late on, despite the visitors throwing men forward, including their goalkeeper, the Robins were unable to breach the home back line and three welcome points were secured.
Blades: Long, White (Hill 77), Maguire, Flynn, Doyle, Porter (Miller 85), Baxter, Collins, Coady, Murphy (Brandy 72), McMahon.
Unused: Howard, Taylor, Cuvelier, Lappin.
Swindon: Foderingham, N. Thompson (Byrne 52), Luongo, Hall, Mason, Pritchard, McEveley, Kasim (Harley 70), L. Thompson (N'Guessan 74), Ward, Ajose.
Unused: Belford, Brango, Elgabas, Gladwin.