After defeats on the two previous visits to Crewe, Unitedites will be satisfied with this victory.
Jamie Murphy made the all-important goal for Stefan Scougall in a second half which also had a missed penalty, a sending off and ten minutes of added time
The Blades dominated and deserved the win and in the process ended Crewe's three match winning run.
Again, boss Clough made three changes. For the encounter at Crewe, McCarthy, Wallace and Baxter returned to the starting line-up. McGahey, Reed and McNulty dropped to the bench. Former Crewe striker Higdon was also amongst United's substitutes.
United knocked the ball around well in the early exchanges and were rewarded with two chances in the opening six minutes, both from Campbell-Ryce crosses. The first saw Baxter turn in the box but his shot was blocked by a combination of Ray and goalkeeper Garratt and moments later, from a corner, Alcock drilled into the ground and his shot beat the goalkeeper, struck the inside of a post before rolling across the box for Tootle to clear.
The first half's possession stats were dominated by the Blades but clear-cut chances after the first 10 minutes were restricted. Campbell-Ryce and Murphy both saw a lot of the ball, whilst Wallace and Scougall attempted to support Baxter at every opportunity.
On 36 minutes a Scougall shot was deflected into the arms of Garratt and Crewe's first effort of the first half arrived a moment later but Howard pushed Cooper's shot around a post.
Also before the break, Murphy's low delivery just failed to find Wallace and in injury-time a free-kick saw Haber's header from 12 yards collected by Howard.
In similar fashion to the first half, the Blades started well after the interval. Campbell-Ryce's run put the home defence under pressure but his subsequent shot with the outside of his boot was wide. He, and Murphy from the other flank, again put balls into the box without reward.
Basham was United's first booking, following a foul on Grant, but United's intent continued.
Murphy's shot was blocked and Wallace fired over, first time, on 56 minutes. Brandy's last effort before being replaced was a shot on 63 minutes which was deflected wide as Crewe broke away.
A Harris shot at pace was blocked but United's persistence paid off on 69 minutes and Murphy played a huge role in the opening goal. The Scottish winger beat Tootle in a 50-yard foot race on the left and waited patiently before laying off to SCOUGALL to sidefoot home.
A lengthy stoppage followed after a clash between Basham, who continued with a bandaged head, and Inman, who was stretchered off after treatment.
When the action resumed the Blades were quickly back on the attack and should have extended the lead. Alcock's ball into the box saw Baxter beat Ray before being upended. Referee Bankes pointed to the spot but Baxter's penalty was pushed around a post by goalkeeper Garratt.
The action continued after Clough made a treble change, introducing McEveley, Reed and McNulty, who had a chance to instantly add to the lead following Ray's mistake but, in a one-on-one situation, the goalkeeper got a vital touch to deflect the ball wide. Ray argued with referee Bankes in the aftermath and was shown a red card.
A Great tackle by McCarthy on Ness prevented Crewe's progress before ten minutes were announced, mainly due to the injuries to Basham and Inman.
In the additional period, Campbell-Ryce shot wide after another impressive run from Murphy but Crewe began to come forward. Grant fired wide from distance, McNulty and Wallace were booked, but the Blades hung on to make it another three points.
Crewe: Garratt, Tootle, Ray, Dugdale, Turton, Inman (Waters 77), Cooper, Leigh, Haber (Haynes 64), Brandy (Ness 64), Grant.
Unused: Shearer, Guthrie, Atkinson, Tate.
Blades: Howard, Alcock, Harris, Wallace, Basham (McEveley 84), Doyle, Murphy, Scougall (Reed 84), Baxter (McNulty 84), Campbell-Ryce, McCarthy.
Unused: Davies, McGahey, Higdon, Turner.