The Blades, backed by over 4,200 supporters, a small portion of whom chanted their support for Evans - albeit on only a handful of occasions with the songs not sung by the vast majority of the visiting support - triumphed thanks toa fantastic 64th-minute striker from Jamie Murphy.
That came a few minutes after United were reduced to ten men after Patrick McCarthy was dismissed for bringing down James Coppinger, with referee Keith Hill pointing to the spot.
But Harry Forrester, who took the penalty instead of regular-taker Nathan Tyson, saw his effort beaten away by Mark Howard.
In the first half, Hill failed to point to the spot after Jamal-Campbell Ryce was felled by Enda Stevens, in a challenge which looked like it took place just inside the area, but instead a free-kick was awarded.
On his side’s win, Clough said: “As a football club, I thought it was a great end (to the week) for the supporters and we had over 4,000 here today.
“We showed the spirit of the club on the pitch and turning up in the numbers they did showed the spirit off the pitch.
“It has been a difficult week and it is lovely to finish it with three points in circumstances of adversity, which is the best way to describe it.
“It has not been easy for anyone at the club, I don’t think. All we can do is our bit on the pitch.”
Clough, who admits to delivering a few candid words to his players at half-time after a subdued first period, added: “We just wanted to be better and I thought we started the second half in the first 15 to 20 minutes was brilliant.
“I thought we started the game okay and then lost our way for half an hour.
“We lost our focus a bit over the penalty. We had a blatant one not given at Walsall and another one today. We have got to learn to deal with them, as frustrating as it is. We can’t lose our focus.”
On Murphy’s sublime winning goal, he added: “The Scottish lads have had a good 24 hours, and the Scottish contingent are pleased with their (international) win and that (Murphy) goal was worthy of winning any game.”
Offering his take on proceedings and explaining why Forrester - not Rovers regular taker with Nathan Tyson on the pitch - Paul Dickov said: “Harry fancied taking it. Nathan had been struggling a little bit as well with his knee and calf. Harry wanted to take it and it was a good strike and great save from the goalkeeper.
“Five minutes in the second half decided it; a crazy five minutes from our point of view.
“They went down to ten men, they got the penalty and we missed the penalty and a few minutes later, they score a fantastic strike.
“After that, we have peppered them a little bit and hit the post and the keeper has made a couple of good saves, but it just wasn’t to be our day.”