Story of the match
Both sides' game plan became glaringly obvious within the opening few minutes, with the hosts hogging possession, whilst Luton Town looked rather dangerous on the break.
It was the bright-starting Hatters who created the opening chance of the game, when James Collins was unable to convert Tom Ince's cross-cum-shot, hitting the post from inside the six-yard box.
In the 12th minute, Teemu Pukki added his 19th Championship goal of the season, firing emphatically past Simon Sluga in the Luton goal, after doing well to keep possession from Todd Cantwell's cut-back.
Both sides continued to threaten in the final third, and it was Pukki who should have doubled his tally and the Canaries' advantage in the 29th minute, but he was unable to direct his left-footed shot past Sluga.
The Finnish striker did extend the home side's advantage in the 43rd minute, tapping home Emi Buendia's deflected shot from inside the six-yard box.
Two minutes later and he could have had a third. Pukki instinctively flung his boot at Buendia's through ball, forcing Sluga into an acrobatic save.
Norwich started the second 45 as dominant as they ended the first, but were unable to carve out an opportunity to see the game off in the opening 15 minutes of the second half.
The Hatters worked themselves back into the game, but in the 73rd minute, Cantwell sealed the victory with a driven effort, beating Sluga at his near post.
Grant Hanley nearly added a fourth for the hosts just two minutes later, picking up possession inside the Luton box, but his guided effort fell the wrong side of the post.
Premier League promotion looking a near certainty
The hosts once again looked brilliant in their seventh successive Championship win.
Going forward they were electric, with Emi Buendia, Todd Cantwell and Teemu Pukki in perfect sync.
The Hatters played well enough and will feel hard done by with a 3-0 loss, but it demonstrated how good Norwich were.
Performances seemingly the main objective for Luton
Luton sit 13 points off the play-offs and 12 from the Championship drop, it now seems that they are in a relatively safe position.
This means that the preparation starts now for next season and building on performances week by week.
For the hosts, Pukki scored his 19th and 20th goals of the season and put in a brilliant performance to go with it.
The Finnish striker did not stop moving and took both his goals expertly. He linked up well with Buendia and Cantwell, as the feared trio looked unplayable at times.
Kal Naismith had another good game in the heart of defence for the visitors.
The utility player has slotted into a central defensive position seamlessly and despite conceding three goals, he did not really put a foot wrong. He won his aerial duels, but he was also clever in possession.