Morris' seventh goal of the season just after the hour ensured a win that lifted Town up to fourth in the table, above their hosts, as they made it seven games unbeaten with a perfect away performance at Carrow Road.
Manager Nathan Jones made three changes from the side that beat QPR at Kenilworth Road on Saturday, with Alfie Doughty making his debut in an attacking role after an injury-delayed start to his Town career since joining from Stoke in the summer.
With the Hatters playing a 3-4-3 formation, Fred Onyedinma came into the starting line-up on the right side of midfield, with James Bree moving inside to centre-half alongside Tom Lockyer and skipper Dan Potts.
Harry Cornick came into the attack for his third start of the season, with former Norwich striker Carlton Morris through the middle, whilst his fellow ex-Canaries Henri Lansbury and Cameron Jerome were amongst the substitutes.
Roared on by a tremendous Tuesday night following of more than 1,200, it was Town - unbeaten in six and on a run of just one defeat in ten matches - who had the game's first chance on eight minutes.
Cornick and Doughty, filling the third attacking role, combined down the left with the latter working the ball across the pitch into Onyedinma's path, but the right wing-back's cross-shot whistled past the far post, just eluding Morris in the six-yard box.
The former Norwich striker provided the second opening 14 minutes in, receiving an Amari'i Vell throw in the Norwich box and rolling Grant Hanley before clipping an inviting cross that flew an inch ahead of Cornick's boot in front of goal.
The third-placed hosts, coming into the game after suffering back-to-back defeats at the hands of Preston and Watford, had to wait until midway through the half for their first shot at goal, and even then it was a 25-yard shot that was well off target from Gabriel Sara as the Hatters defended with great discipline.
Their second attempt, in the 26th minute, was much more accurate with Josh Sargent smashing a left-footed volley at goal from outside the area, but the striker's USA international team-mate Ethan Horvath was equal to it.
It was Sargent's strike partner Teemu Pukki who had the next chance, but not until two minutes before half-time, as he broke away from the Town defence, but with James Bree racing back to pressurise him, the Finnish forward fired high over the bar from 15 yards out.
Doughty set Cornick sprinting clear with 45 minutes on the clock, and after checking back onto his left foot as he enterred the box with just goalkeeper Angus Gunn between the forward and his first goal of the season, his attempted pass to Campbell was smuggled away by the Canaries' defence.
Norwich boss Dean Smith brought Todd Cantwell on in place of Sargent, who had been down for treatment in the first half, and it was his side who had the first sight of goal in the second period, Danel Sinani firing over the bar in the 46th minute, before Aaron Ramsey did the same ten minutes later.
Morris and Bell saw shots blocked at the other end as the Hatters continued to ask questions on the break, and it was Morris who broke the deadlock just after the hour, mesmerising the retreating Grant Hanley with a couple of step-overs as he progressed into the box before curling a beauty into the bottom corner for goal number seven of the season.
There was no celebration from the Town top scorer in recognition of the role Norwich played in his development.
Jones made two changes straight away, bringing on skipper Sonny Bradley for Onyedinma, and Jerome for Cornick, with the ex-City striker receiving a warm reception on his first return to Carrow Road since leaving for Derby in 2018.
Norwich went close to levelling with a Sara shot that Horvath pushed behind, and it was from the resulting corner that the hosts were reduced to ten men when Kenny McLean hit Lockyer in the face as they waited for the delivery.
Jones made two more changes on 77 minutes, replacing the goalscorer with Adebayo and the excellent Doughty with Luke Freeman.
Norwich had plenty of possession without really creating a chance, Pukki firing a 20-yarder that Bradley got his head on, the ball shooting straight up in the air and into Horvath's grateful arms, before the Finn then curled wide with a better opening with ten minutes left.
Freeman had a great chance to double the advantage when Campbell picked his fellow midfielder out with a cross from the right, but the former Bristol City and QPR man's volley hammered into the ground and wide, before Campbell shot straight at Gunn moments later.
Former Town youngster Max Aarons cut in from the right with five minutes left, but this time it was Lockyer sticking his head in the way to deflect it over the bar.
Eight minutes of stoppage time were announced, and the Hatters saw them through with relative ease to leapfrog their opponents and move up to fourth in the table ahead of another huge game on Sunday.
Goal:
Morris 62'
Att: