The Canaries had to work harder for their win than they did on Tuesday, when they hammered Plymouth 6-1, but it was a deserved success against a Luton side who contributed to their own downfall with some poor defending.
Having gone behind to a soft goal from Elijah Adebayo, Norwich turned the game around before the break with two goals from Ante Crnac.
Luton hit back just after the interval through Jacob Brown, but two late goals from Emiliano Marcondes and Borja Sainz condemned the visitors to a sixth straight away defeat.
"When we went behind, and then lost the lead, the fans were always there giving their support and we were really grateful for that, it really helped us across the line," Thorup said.
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