Elijah Adebayo netted his seventh goal of the season in the 17th minute to earn a third win from those five matches, although the top scorer limped off injured at the break, with Luke Berry having already gone off in the opening period with a knock.
Manager Nathan Jones had made two changes to the team that drew 2-2 at Derby on Tuesday night, Fred Onyedinma starting on the left-hand-side and Berry coming into midfield, with Kal Naismith missing out through suspension and Pelly-Ruddock Mpanzu on the bench.
Town came agonisingly close to taking a fourth-minute lead when Berry's close range shot was deflected onto the post off a combination of Onyedinma and Hull defender Lewie Coyle, whose team-mate Jacob Greaves managed to smuggle the ball behind for a corner.
Town had a deserved lead by the 17th minute, Onyedinma's dancing feet creating the space to deliver a beautiful bending cross to the far post, where Adebayo headed into the roof of the net for his seventh goal of the season.
Two minutes later, in the 19th, a rapturous tribute for Jacob Crawshaw, the 19-year-old Town supporter who tragically lost his life in a road accident hours after watching the Hatters win at Millwall last Saturday, took place with fans on all four sides of Kenilworth Road standing to applaud.
By the 21st minute, Town were forced into a change - Berry suffering a knock in a challenge on the edge of the Luton penalty area, and having to be replaced by Mpanzu.
The visitors' centre-half Di'Shon Bernard, on loan with the Tigers from Manchester United, because the first player into referee John Busby for pulling Adebayo back as he looked to latch onto a pass from Clark on halfway.
It was symbolic of a scrappy period of the half, but the Hatters burst back into life in the 39th minute when Adebayo fed Cornick, who laid the ball back for Onyedinma to curl another lovely cross towards the Hull six-yard box.
Clark jumped in front of keeper Matt Ingram, who strangely chested the ball clear but only as far as Glen Rea, who cracked a volley goalwards, only to be denied by a terrific recovery save by Ingram.
Rea was having an excellent half on his fifth successive start since being reintroduced to the team by Jones for the win over Coventry last month, as was Adebayo - although the goalscorer would become the second change at the break, going off injured and replaced by Cameron Jerome.
A slow start to the second period ensued before Clark stung Ingram's palms with a 20-yard drive just before the hour mark, then Bradley had to make two vital interceptions - one a brave header, the second a block - to help keep the scoresheet blank at the other end.
Hull had threatened briefly at the end of the first half, Mallik Wilks firing straight at Simon Sluga, and striker Josh Magennis headed wide from a Richard Smallwood cross as they enjoyed more territory in the second.
They introduced former Hatter George Moncur shortly after, the attacking midfielder's contribution to our League One championship success and establishment in the Championship recognised by a warm reception from the home fans as he replaced Wilks in the 64th minute.
Rea made another vital contribution, this time in his own box, on 74 minutes as Hull sub Tom Eaves looked to set up Keane Lewis-Potter for a shot after gathering a loose ball following slight hesitation by Sluga.
Jones withdrew Onyedinma in the 78th minute, replacing him with centre-half Reece Burke, who made the opposite move to Moncur in the summer transfer window, joining the Hatters after helping Hull win promotion from League One.
Cornick looked to latch onto a knock-down from Jerome with just over ten minutes to go, but it had proved a frustrating second half to that point for the Town, with the early substitutions having seemingly disrupted the team's rhythm.
Still, a fourth clean sheet in five matches - and seventh of the season - would ensure three points and Jerome did his bit to help that with a header clear as Hull piled pressure on late on, before Greg Docherty fired across goal and wide in injury-time.
Goals:
Town: Adebayo 17
Att: 9,999 (793 away)