Luke Berry scored the opener in the first half before Jack Marriott replied for Derby early in the second half. But with three minutes remaining, Jordan Clark scored his second winning goal of the week to ensure Town again came out on top and moved up to second place in the Championship.
Nathan Jones named an unchanged line-up from last weekend’s Championship opener against Barnsley and the Hatters enjoyed a good opening spell, creating several chances from the 20th minute onwards.
First of all, Martin Cranie picked out Harry Cornick with an inch-perfect ball forward, the wide-man got the ball on his left and struck low, but it hit the base of the post.
Just seconds later, Cornick was looking to provide for his team-mates and drilled a cross into the box, but James Collins couldn’t stretch far enough to turn the ball home.
The same routine almost worked again, though this time Andre Wisdom made a vital intervention for Derby just as Collins was about to connect with Cornick’s cross.
However, it wasn’t before long that the Hatters did manage their deserved breakthrough and it came courtesy of Berry in the 34th minute.
Elliot Lee crossed from the left-hand-side and Berry beat David Marshall to the ball and poked it into the back of the net from close range.
Derby found a route back into the game as Marriott picked out the bottom corner from inside the box, seven minutes into the second period.
Town were eager to regain their lead and Lee came close to doing just that. Half-time substitute James Bree found space on the right and crossed low for the former Barnsley man, but his effort went just wide of the goal.
The Hatters also had to be wary of Derby’s attack threat as Jamal Hector-Ingram came off the bench and almost had an immediate impact, though Sluga was out quick to block his effort.
In the 87th minute, the Hatters struck again as Rhys Norrington-Davies stood a cross up to the back post and substitute Jordan Clark was there to head into the net.
With the last kick of the game in the six additional minutes, Wayne Rooney went agonisingly close to equalising once more but Sluga was relieved to see the ball go wide of the post.
Town will now look to make it five wins in a row when they face Manchester United in the third round of the Carabao Cup on Tuesday.
Town: Sluga, Cranie, Pearson, Bradley (C), Norrington-Davies; Rea (Bree 46), Berry, Mpanzu, Lee (Clark 83); Cornick (Moncur 83), Collins.
Subs not used: Shea, Hylton, Shinnie, LuaLua.
Goals: Berry (34), Clark (87)
Yellows: Norrington-Davies, Mpanzu
Derby: Marshall, Byrne, Wisdom, Clarke, Forsyth; Shinnie (Sibley 45), Bird; Jozwiak (Whittaker 88), Rooney (C), Knight, Marriott (Hector-Ingram 64).
Subs not used: Roos, Evans, Buchanan, Davies
Goals: Marriott (52)
Referee: Dean Whitestone