Defender Anthony Gerrard scored the only goal of the game midway through the second half from Robert Koren's inswinging corner.
Nigel Pearson's side are now nine league games unbeaten and up to eighth in the table on the strength of only one defeat in their last 18 league matches.
Derby have not won in their last eight Championship outings and have been beaten in six of their last seven home fixtures.
Tomasz Cywka was recalled to the Rams starting line-up in place of Paul Green, who missed out with a knee knock.
That was the only change from the goalless draw at Scunthorpe on Saturday, so on-loan Jamie Ward made his home debut. Fellow forward Theo Robinson, signed on loan from Millwall on Tuesday, started on the bench.
Hull also made a solitary change. Cameron Stewart suffered knee ligament damage at Ipswich at the weekend, so James Harper was recalled.
Miles Addison missed the target with a header early on before former Hull loanee Daniel Ayala did likewise as Derby threatened again in the 19th minute.
Ward was next to go close with a header just before the break.
Derby were forced to replace goalkeeper Stephen Bywater at the start of the second half, with James Severn coming on for his first league appearance for the club.
Hull were obviously keen to test the youngster early on and Matty Fryatt and Aaron Mclean shot from the edge of the box but both failed to work Severn.
That was not the case in the 57th minute when the substitute had to parry a Mclean effort.
At the other end, Bradley Guzan produced a similar save to thwart Cywka.
Gerrard broke the stalemate in the 71st minute. The defender netted for the third time this season from close range following Koren's curling delivery.
Derby desperately searched for an equaliser, with Ayala and Ben Davies forcing Guzan into saves in the final 10 minutes.
But Hull held out and remain unbeaten on their travels in the Championship since the end of September.