Only the top three of Newcastle, West Brom and Nottingham Forest - all of whom have failed to win at Pride Park - have notched more home wins than Derby, who are now nine points above the relegation zone with six matches remaining.
Leicester are without a win in three games but stay in the play-off position despite falling a place to sixth.
Dean Leacock made his first start for the Rams in over three months as one of two changes made by Clough.
The defender suffered a knee injury in December but, after three substitute appearances, returned to the side in place of Nicky Hunt.
The other switch saw Steve Davies recalled at the expense of on-loan Arsenal forward Gilles Sunu, while new loan signing Tomasz Cywka started on the bench.
Leicester made three changes. Defenders Wayne Brown and Chris Powell came in for Ryan McGivern and Nolberto Solano, while striker Yann Kermorgant was handed his first start for two months in place of Paul Gallacher.
There were few chances in the first half and the goal, when it arrived, came as something of a surprise.
Davies' attempted one-two with striker partner Chris Porter on the edge of the box was read by Foxes midfielder Andy King, who played a routine back-pass to his goalkeeper Chris Weale.
However, as Weale tried to control the ball it rolled over his foot and into the unguarded net.
Leicester's only response in the opening 45 minutes came just before the break when County keeper Stephen Bywater tipped a 20-yard shot from Richie Wellens around a post.
Derby flew out of the blocks in the second half with Michael Tonge going close with a shot from the edge of the box before Porter threatened on three occasions from a similar distance.
Foxes boss Nigel Pearson responded by bringing on Gallacher and former Ram Steve Howard just after the hour mark, with Kermorgant and Martyn Waghorn the players to make way.
Wellens had two efforts in quick succession midway through the second half, missing the target with the first but working Bywater the second time.
Sensing his side were making some headway, Pearson made his final substitution with 15 minutes remaining taking off midfielder Matt Oakley and introducing forward Dany N'Guessan.
And the former Lincoln youngster almost made an immediate impact but headed Gallacher's far-post cross over the bar.
Gallacher was the instigator once more when Michael Morrison had Leicester's final chance to rescue a point but the defender's effort was saved by Bywater late on.