Elijah Adebayo's first-half goal, his 14th of the campaign, was enough to complete the double over fellow play-off chasers City as Nathan Jones' side continue their quest to feature in the race for promotion to the Premier League.
The win, a fourth successive success on a midweek away day in 2022 following successes at Reading, Swansea and Stoke, takes Town up to sixth place and keeps the Sky Blues six points below them in 11th.
Manager Nathan Jones made five changes to the team that lost 2-1 at Middlesbrough on Saturday, with Dan Potts coming into defence after starting recently against Chelsea in the FA Cup, with Kal Naismith absent.
Pelly-Ruddock Mpanzu returned to the midfield as captain after missing the last four matches, joining Luke Berry and Jordan Clark - the latter of whom was starting for the first time since the 2-0 away win against Reading, and after scoring his tenth goal in all competitions on Saturday, Harry Cornick came in to start alongside Adebayo.
The hosts came out of the traps quickly, Viktor Gyokeres breaking down the right and crossing low for Matty Godden to steer an effort on target within 13 seconds of the kick-off. Palmer saved that one comfortably, before Gyokeres blazed over from the left side of the penalty area with just three minutes on the clock.
Adebayo led the Town's first attack down the right, cutting the ball back in the direction of strike partner Cornick, with Clark retrieving it and standing up a cross to the far post, where Todd Kane headed behind for a corner.
From the set piece, the Sky Blues cleared and broke quickly, with Amari'i Bell becoming the first name into referee Oliver Langford's notepad on eight minutes for pulling back Ian Maatsen as he looked to get in on goal.
Berry had the Hatters' first attempt on target in the 27th minute, but home keeper Simon Moore was right behind the the 25-yard curler, before another opening came his way just after the half-hour, Coventry managing to block and clear as the midfielder prepared to latch onto Cornick's long throw.
Palmer had to be alert to keep out a near post shot from Kane as the Sky Blues broke immediately down the right, then the hosts appeared fortunate to still have 11 men on the pitch as Jamie Allen clattered into Berry with his arm, ref Langford choosing to only show yellow.
Palmer was soon to play a crucial role at both ends of the pitch as the Hatters took a 38th-minute lead. Just seconds after saving well from Gyokeres, after Gustavo Hamer had played the Swede in on the left side of the box, the West Brom emergency loanee played a long ball forward that home centre-half Michael Rose misjudged.
Adebayo was alive to the opportunity and took the ball into the Coventry area, then slid a right-footed shot beyond Moore and inside the far post for his 14th goal of the season.
Coventry came out after the break seeking an equaliser, Kyle McFadzean heading over from Hamer's free-kick, then Maatsen cut in from the left and hitting one that was thankfully too high with 55 minutes gone.
The Hatters had the ball in the net again just after the hour, with Potts tapping in after Adebayo's shot had been saved by Moore, then turned goalward again by Lockyer, but the Town defender was in an offside position as he finished from close range.
Clark was having a terrific game in the Town engine room and a brilliant 50-yard run, in which he twice stayed on his feet when Coventry players tried to bring him down, almost put Cameron Jerome into the byline, but the sub - on for Cornick - had just strayed offside.
Jones made his second switch with 20 minutes to go, bringing Allan Campbell on for Berry, another of the returning midfield trio who had put in a tremendous shift alongside Mpanzu and Clark.
Gyokeres tried his luck with a right-footer from the left side of the Town area with 15 minutes to go, but Lockyer got his head in the way and deflected the ball behind for City's first corner of the night - which Palmer also watched gratefully sail over his crossbar.
The irrespressible Clark then tricked his way past his man on the left, sending in a teasing cross that was just too high for Adebayo at the far post, before Palmer made another wonderful save from point-blank range as Callum O'Hare burst into the box with ten minutes to go.
Clark made way for Henri Lansbury with six minutes left, as Jones looked to cement the result, and Adebayo was soon tricking his way down the left and drawing Coventry skipper McFadzean into a foul that led to a yellow card.
Bree whipped the free-kick across City's six-yard box, but Moore gathered as a host of Town attackers looked to pounce.
Coventry could find no way past a stubborn Town backline, with Maatsen's injury-time header finding only the side-netting and the Hatters ensuring they still haven't lost back to back league games all season, to the delight of the 1,757 travelling supporters.
Onto Sunday lunchtime and the visit of QPR to Kenilworth Road!
Goals:
Adebayo 38
Att: 16,996 (1,757 Hatters)
