The hosts had led through Allan Campbell’s 22-yard strike just after the hour mark, before Teemu Pukki quickly levelled.
Substitute Cauley Woodrow then came off the bench to score a last minute winner as Rob Edwards picked up a first victory since taking over as manager.
To find out how the hosts rated on the evening, see below.
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Luton's players celebrate Cauley Woodrow's last minute winner against Norwich Photo: Liam Smith
. Ethan Horvath: 7.5
Although Norwich had a lot of the ball at times, he didn't have a great deal to do in the first period, bar parrying Sara’s swerving piledriver away. After the break, Luton’s defence kept the City attackers out until Potts’ slip, although might feel he could have got something on Pukki’s attempt. Batted away McLean’s deflected shot, before being able to watch some late attempts bounce wide. Photo: Liam Smith
. James Bree: 8
Early set-piece was almost turned in to give Luton the lead, before his terrific free kick nearly put the Hatters ahead, tipped on to the bar by City keeper Gunn. Put in a real shift on the right hand side for the Hatters throughout the 90 minutes, showing great energy to get up and down the flank. Photo: Liam Smith
. Gabe Osho: 8
Had defended with real intent for large parts of the game, as Luton kept a strong Canaries side at arm's length. Picked up an incredibly harsh yellow card when he clearly won the ball and paid the price for the referee’s error with 10 minutes to go as a second booking for tripping Pukki meant he was sent off for the second time this season. Photo: Liam Smith
. Tom Lockyer: 9
Once more he was the stand-out performer in the Hatters' back three. Showed some real class when up against Pukki, barely letting him get a shot in during the first half. His ball forward led to Luton’s opener after the break, as he should have been on target himself, heading off target twice. With the hosts winning, he was there to lead Town’s defensive efforts in keeping the Canaries out in what was a frantic final few minutes. Photo: Liam Smith
1. Ethan Horvath: 7.5
Although Norwich had a lot of the ball at times, he didn't have a great deal to do in the first period, bar parrying Sara’s swerving piledriver away. After the break, Luton’s defence kept the City attackers out until Potts’ slip, although might feel he could have got something on Pukki’s attempt. Batted away McLean’s deflected shot, before being able to watch some late attempts bounce wide. Photo: Liam Smith
2. James Bree: 8
Early set-piece was almost turned in to give Luton the lead, before his terrific free kick nearly put the Hatters ahead, tipped on to the bar by City keeper Gunn. Put in a real shift on the right hand side for the Hatters throughout the 90 minutes, showing great energy to get up and down the flank. Photo: Liam Smith
3. Gabe Osho: 8
Had defended with real intent for large parts of the game, as Luton kept a strong Canaries side at arm's length. Picked up an incredibly harsh yellow card when he clearly won the ball and paid the price for the referee’s error with 10 minutes to go as a second booking for tripping Pukki meant he was sent off for the second time this season. Photo: Liam Smith
4. Tom Lockyer: 9
Once more he was the stand-out performer in the Hatters' back three. Showed some real class when up against Pukki, barely letting him get a shot in during the first half. His ball forward led to Luton’s opener after the break, as he should have been on target himself, heading off target twice. With the hosts winning, he was there to lead Town’s defensive efforts in keeping the Canaries out in what was a frantic final few minutes. Photo: Liam Smith