Inform Jamie Murphy and Matt Done were on target again as the Blades made it three wins on the bounce.
In a tough tussle at Meadow Lane, Murphy scored his fifth in six games since signing a new contract and Done added his fourth in three games since joining Nigel Clough's Blades.
Injuries forced manager Clough into two changes. McEveley and Baxter missed out due to problems picked up at the weekend, Reed and Holt came in. Loan Scotsman Holt was making his first Blades start and began just behind striker Done.
All the home side could show for their early endeavours was a wayward effort from Dumbuya, whilst United's early threat came from Brayford's pace down the right, which paved the way for Murphy shooting wide on nine minutes.
It was from the left, however, that United made the breakthrough on 16 minutes and a contributory factor was the home defenders switching off. A quick throw from Harris enabled MURPHY to cut inside his marker and beat Carroll with a powerful shot into the far corner.
Just two minutes later and with a move similar to the goal, Holt cut inside from the left but Carroll saved with his chest and soon after Done's first-time, sidefoot volley was just wide from 20 yards.
The goal inspired United, who were the more dominant force for much of the first half - Done had another chance after turning Mullins but his shot was across goal and wide.
For Notts, Bajner was under pressure as he flashed a shot wide but there was an element of luck as they levelled on 35 minutes. A cross from the right saw Brayford's clearing header unfortunately hit Reed and drop invitingly for NOBLE to score with a backheel from close-range.
United won a couple of corners before the break, but the goal gave Notts impetus and they went close again on 40 minutes when Gary Thompson chested down and volleyed over.
An open start to the second half suited Notts and gave them the early momentum. Carroll was quick off his line to clear and set Gary Thompson free between Kennedy and Harris but Turner made a vital save, sticking a leg out and kicking clear. Brayford was also forced to make a couple of blocks in the first five minutes after interval.
The home side certainly made the better start to the second period and Holt was the first in the book for cynically stopping a potential breakaway. On 61 minutes, from Gary Thomoson's cross, Bajner went close at the near post.
Just after the hour mark, McNulty replaced Reed and there was minor reshape in United's forward positions, which included Coutts moving to a central role. Kennedy was booked following a solid challenge on Bajner but United weathered the storm and began to push the home side back again.
Notts, themselves, were also defending solidly, keeping the Blades at arm's length... that was until the referee's watch was about to tick around to 15 minutes left. It was then that Murphy and Harris combined on the left, resulting in the latter delivering a low cross which DONE connected with and put just enough spin on the ball to deceive Carroll and trickle over the line.
Soon after Done's pace set up McNulty and as the clock ran down Clough introduced Alcock and Freeman to sure up the defensive unit. Noble tried his luck from distance late on and five minutes of added time gave the home fans hope.
However, they did not bank on United's disciplined professionalism and the added minutes were comfortably negotiated to send home the 2,936 Blades fans home happy.
Notts County: Carroll, Dumbuya, Adams, Mullins, Edwards, Hayhurst (Newton 78), G. Thompson, Jones (Woolery 78), C. Thompson, Noble, Bajner.
Unused: Pilkington, Hollis, White, Daniels, Harrad.
Blades: Turner, Harris, Brayford, Basham, Doyle, Murphy, Done (Freeman 89), Coutts, Reed (McNulty 63), Kennedy, Holt (Alcock 86).
Unused: Willis, Davies, Campbell-Ryce, Adams.