Clarke headed in a second-half corner to settle a game low on quality and the centre-half also made a crucial block to deny Herbie Kane an equaliser.
Jarrod Bowen missed a glorious first half chance for Hull but the visitors created little after that as Derby, who were charged on Thursday by the EFL for a breach of spending rules and also lost midfielder Krystian Bielik with a season-ending knee injury, held on for a third successive home win.
Derby brought in Tom Huddlestone and the former England midfielder set up a chance in the sixth minute when he played in Jayden Bogle who forced George Long into a diving save.
Jarrod Bowen was getting into some dangerous positions but the final ball was letting Hull down and Callum Elder wasted a good opening with an overhit cross before the visitors missed a great chance in the 25th minute.
Herbie Kane did well near the byline to pull the ball across and when it fell to Bowen eight yards out, he looked certain to score but he dragged his shot wide.
Bowen held his head and there was a worrying moment for Hull when he was caught late but was able to continue after treatment.
Wayne Rooney had been on the periphery of the action but he almost played in Jason Knight in the 33rd minute and he set up Martyn Waghorn for a shot which went wide eight minutes later.
Derby ended the half strongly with Rooney just failing to clear the defensive wall after he was fouled a couple of yards outside the area but it had been a disjointed opening 45 minutes.
Both sides continued to give the ball away at the start of the second but there was panic in the Hull defence in the 57th minute when Bogle wriggled past two challenges before he went over but referee Andy Woolmer decided there was no contact.
Derby went in front in the 64th minute when Long came for a Tom Lawrence corner but Clarke got their first to head into an empty net.
Hull were almost handed an equaliser in the 70th minute when Ben Hamer and Huddlestone lost the ball to Kane but his goal-bound shot was blocked by Clarke.
There was a vital block at the other end in the 80th minute when Bogle whipped in a low cross but Waghorn's shot was charged down and when Hull tried to counter, Martin Samuelsen fired wildly over.