The Rams took an early lead through Lee Gregory before Graeme Shinnie’s penalty early on in the second half put the Hatters out of reach as they were unable to mount an unlikely comeback.
Manager Nathan Jones named an unchanged team for the third consecutive game, with Glen Rea dropping into the middle of a back three.
After an even opening five minutes, Derby took an early lead through Gregory. Louie Sibley delivered towards Martyn Waghorn at the back post, whose first time touch across the six-yard box found the onrushing Gregory, who finished from close range.
Following a disappointing start the Hatters created their first opportunity of the afternoon. Kiernan Dewsbury-Hall found Jordan Clark down the left, delivering a floated cross towards Elijah Adebayo, who was able to out-jump Matt Clarke at the far post but couldn’t direct his header towards goal.
After struggling to gain a foothold in the early stages of the game, the Hatters should have drawn level midway through the first half. Town broke from inside their own box with Cornick and Dewsbury-Hall driving forwards at pace, the latter releasing Adebayo but his first-time shot was saved brilliantly by Derby stopper David Marshall with his foot.
Luton began to gain control of proceeding at a sunny Pride Park and Jordan Clark’s crosses from the left continued to cause problems, this time delivering right footed to find Glen Rea at the near post who flicked on, but his effort was turned behind for a corner by Marshall.
The Hatters went into the half-time break in the ascendancy but without anything to show for it on the scoreboard after enjoying an extended spell of pressure in the latter stages of the opening period.
Luton’s plans for a second-half fightback were thrown into disarray three minutes in, however, after Glen Rea conceded a penalty that Graeme Shinnie converted to double the Rams’ lead, leaving the Hatters with it all to do if they were to salvage anything from the game.
Town manager Jones reacted by switching back to a diamond and introducing former Derby man Tom Ince in an attempt to add some creativity to the Luton ranks, whilst also freshening up the front two by turning to Sam Nombe and James Collins with 20 minutes remaining.
The Hatters continued to probe and press in search of goal that would give them a fighting chance to pick up some points, but weren’t able to test ‘keeper Marshall as Derby held firm and denied the visitors any shots on goal.
In a second half where the Hatters failed to register a shot on target, Matty Pearson came closest with a header from inside the box but he was unable to head it down towards goal as the Town struggled to create any clear-cut chances.
Luton will be looking to bounce back on Easter Monday at Kenilworth Road as they face in form play-off hopefuls Barnsley.
Town: Sluga, Clark, Pearson, Naismith, Bree, Rea (Ince 57), Mpanzu, Dewsbury-Hall (Berry 82), Tunnicliffe, Adebayo (Collins 70), Cornick (Nombe 70)
Yellows: Pearson, Dewsbury-Hall
Subs not used: Shea, Cranie, Moncur, LuaLua, Morrell
Derby: Marshall, Wisdom, Forsyth, Shinnie, Bird, Waghorn (Kazim-Richards 45+1), Lawrence (Buchanan 84), Byrne, Clarke, Sibley (Knight 62), Gregory (Jozwiak 62)
Goals: Gregory (7), Shinnie (49 Pen)
Yellows: Wisdom, Byrne, Sibley, Kazim-Richards
Subs not used: Roberts, Mengi, Roos, Baningime, Watson