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Paul Warne was the star of the show for the Millers, scoring his side's first goal in first-half stoppage time, before setting up the winner for Kevin Ellison.
Rotherham beat three Championship sides last season but it was not easy to see why as they started sluggishly against Clough's Derby.
Gary Teale grabbed his second goal in just two games after 11 minutes as the Rams looked set to cure their recent away day blues, which has seen them win once on their last seven away trips.
Lee Croft supplied the ammunition and Teale the finish as Derby threatened to run riot in the early stages against Rotherham.
The goal kick-started Rotherham and Nicky Law and Pablo Mills both had efforts on goal as the home side started to get a foothold in the game.
Goalkeeper Andy Warrington ensured Rotherham didn't fall any further behind as he clawed away a Ben Pringle free-kick on 35 minutes.
Rotherham deservedly drew level in first-half stoppage time as veteran striker Warne - in his second spell with the club - pounced on a loose ball six yards out to force the ball home.
After the break it looked as though there was only going to be one winner as Ellison and Warne started to cause Derby's lacklustre defenders all sorts of problems.
On 65 minutes Warne squeezed his way into the Derby penalty area, before laying the ball off to Ellison to slam home from eight yards.
Rotherham stepped back into their shell in the final quarter and their goal led a charmed life as a result as Robbie Savage's free-kicks and probing high balls caused chaos in the home defence.
As Derby threw the kitchen sink at Rotherham late on, Warne, who was at the centre of all that was good about the Millers, broke clear and was left bemused as the official failed to spot Dean Moxey using his arm to halt the ball.
Derby looked to have got out of jail in the last minute as Jake Buxton's header looked goalbound but not for the first time Warrington came to Rotherham's rescue and produced a brilliant fingertip save.