Clough, who succeeded Paul Jewell at Pride Park at the start of the year, watched his side claim a crucial three points in their battle against relegation with something of a smash-and-grab win.
Chris Porter had given the Rams the lead after only 52 seconds, but City's relentless pressure was finally rewarded when Gavin Williams equalised with a superb 25-yard volley in the 84th minute.
However, parity lasted little more than 90 seconds before Rob Hulse struck the decisive blow of a thoroughly entertaining encounter.
It was in stark contrast to the home game against Swansea on Wednesday night when a dominant Derby display was rewarded with only a point after a late equalising goal for the Welsh side.
On his fifth league victory as manager, Clough said: "Without a doubt it is the most pleasing three points since I have been here.
"It was the way we achieved it without playing great and taking the game to the opposition, and all the other qualities that we hadn't shown in abundance in the last few weeks came to the fore.
"In some ways I think it has evened itself out after midweek. The way the games went you might have thought we would have got three points on Wednesday and a point today, but it turns out the other way around.
"Although we spent the majority of the game defending, in the second half we still created some very good chances.
"Albeit they were on the break, and even though we don't particularly want to play like that, especially in front of our own supporters, needs must I'm afraid."
Goalscorer Porter had to go off at the break with a hip injury, forcing Clough into a reshuffle.
He was replaced by Andy Todd and the centre-half was used as a holding midfielder as the Rams adopted a rigid 4-5-1 formation, with Gary Teale occasionally supporting Hulse.
Jay McEveley is now also nursing a hamstring problem and joins an injury list that includes Miles Addison, Steve Davies, Kris Commons and Paul Green.
Clough hopes to bolster his squad with a loan signing before his side travel to St Mary's to face relegation rivals Southampton on Tuesday evening.
He added: "Chris Porter got a knock on his hip just before half-time and although we had a couple of strikers on the bench, we thought we might need Andy Todd a bit more.
"We hope it's not serious but we will have to see how it settles down on Monday.
"Jay McEveley has a tight hamstring so that's another two to add to a growing injury list.
"It will see our efforts to get someone in on loan step up and we hope to do that by Monday."
Bristol City boss Gary Johnson was so incensed by his side's midweek defeat to Birmingham that he did not attend the post-match press conference at St Andrew's.
The Londoner did face the press at Pride Park, but admitted that his mood had not improved following another away defeat that provided another setback to City's play-off aspirations.
However, Johnson insisted his side could take some positives into their home game against Coventry on Tuesday night.
"It has not improved my mood because whenever you lose you are going to be disappointed," said Johnson.
"But sometimes it is the way you lose and we lost better here as against Birmingham we really didn't give it a go.
"We had a lack of concentration in the first minute but it gave us 80-odd minutes to get back into the game and I think the lads did everything they could apart from sticking the ball in the back of the net.
"We had plenty of opportunities but goals count and although we had all the possession and chances and crosses into the box, it doesn't help us with the three points.
"But what it does do is help us to go into the next game knowing that we have got our football back a little bit."