On this occasion Norwich had as 2-0 advantage at the break and this was the final score thanks to a solid defensive performance which denied Luton any clear-cut chances in a more even second half.
In a highly-competitive game the major controversy came after the final whistle when referee Kevin Wright showed a red card to Luton captain Kevin Nicholls for an alleged gesture towards the home fans.
The visitors kicked off attacking the River End but were a goal down by the third minute.
Dean Ashton picked out Andrew Hughes with a square pass and the City captain opened his account for the club with a fierce right-foot drive from 16 yards which flew over Marlon Beresford's shoulder and into the back of the net.
Six minutes later Ashton again found Hughes but this time the midfielder's diagonal cross drifted out of play beyond the far post.
Youssef Safri was booked for dissent after 23 minutes but the Canaries were soon on the up again.
Just two minutes later Robert Green's goalkick found Darren Huckerby via Peter Thorne's head and he beat the advancing Beresford with a low right-foot shot from 12 yards.
The next time the Luton keeper came off his line he caught Adam Drury's boot as they both went for a through ball.
In the 37th minute Gary Doherty headed Safri's free-kick over the angle of the post and bar then Marlon Beresford did well to hold Ashton's powerful shot from 20 yards
Early in the second half Etuhu, Huckerby and Ashton had goalbound shots blocked by defenders.
After that the game was evenly balanced but in the 90th minute Russell Perrett was shown a second yellow card to make it a disappointing day for the large contingent of travelling fans.