A youthful Blades team took the derby bragging rights, thanks to a 90th minute penalty.
Ben Davies held his nerve to convert but full credit must go to the young the Blades team which, at one point contained two 18-year-olds and a 16-year-old!
Rotherham, without a win at Bramall Lane since 1980, saw a 16-match unbeaten run come to an end.
As expected, Clough made changes - no less than eight in total. Only Maguire, McGinn and Freeman remained from Saturday's draw with Leyton Orient, amongst the incomers was 18-year-old Dimaio, an Academy prospect, who made his full debut in central midfield.
Quickly evident was that the home side were operating with a different formation. Hill, Maguire and Kennedy were the back three with Freeman and Harris in wing-back roles. McGinn, Davies and Dimaio made up the midfield with Baxter and Paynter the front two.
The initial noise from the away fans soon subsided and in an even first 15 minutes the opportunities of note fell to the Blades. McGinn's shot was blocked by Morgan and then the Scotsman fired over, as did Baxter from long-range.
Rotherham hit back with a number of good chances as the half progressed. Tavernier was enjoying a fair amount of space and his powerful shot was pushed away by Long, whilst Agard took Revell's header off the boot of team-mate Hitchcock.
The chances as the break approached were all for the visitors, whilst Harris was shown a yellow card for a full-blooded challenge on Hitchcock. Long was out quickly to smother from Hitchcock and, on the stroke of half-time, the goalkeeper was almost embarrassed when his clearance struck the same Rotherham striker - fortunately, the ball ricocheted wide.
The second half began with two penalty shouts for Rotherham but referee Dean was uninterested. The visitors, however, continued their momentum from the first half, although Long was barely tested and, at the other end, Collin had to collect a Maguire header from a Davies corner.
Khan replaced Harris just after the hour and immediately saw a lot of ball. McGinn fired over on 70 minutes and then a blast from Baxter had hearts in mouth but the shot was just wide.
Baxter was replaced soon after - his place taken by 16-year-old Reed, who slotted into the midfield and with three teenagers on the pitch, the Blades were holding their own. Coady replaced Dimaio late on but the drama was to follow.
As a corner was coming in referee Dean was looking directly at the contact between Morgan and Maguire and even warned the pair. Morgan did not heed the warning and after pulling the Blades stand-in skipper the man in the middle took his time and pointed to the spot. Rotherham's persistent complaints fell on deaf ears and DAVIES took his time before sending the goalkeeper the wrong way as the watch ticked around to 90 minutes. The scorer was booked for taking off his shirt in celebration but was not bothered.
Four minutes of injury-time saw Rotherham resort to long-ball but they were unable to penetrate the young Blades defence, who remained solid.
Blades: Long, Harris (Khan 64), Maguire, Hill, Baxter (Reed 73), McGinn, Paynter, Davies, Freeman, Kennedy, Dimaio (Coady 87).
Unused: Brayford, Scougall, Murphy, Willis.
Rotherham: Collin, Skarz, Arnason, Revell, Milsom (O'Connor 52), Pringle (Vuckic 83), Morgan, Agard, Tavernier, Hitchcock (Thomas 74), Smallwood.
Unused: Shearer, Brindley, Davies, Adams.