First-half goals from Hannibal and Jaidon Anthony got the Clarets on their way as they enjoyed a dominant first-half.
The Canaries set up a nervy finish when Jack Stacey halved the deficit late on, but Scott Parker’s men held on for the three points.
With Sheffield United losing to bottom side Plymouth Argyle on Saturday, the Clarets remain five points ahead of the Blades in third with only four games remaining.
The two promotion rivals do face off at Turf Moor, however, on Easter Monday.
Can you spot yourself in our gallery of fan pictures from Friday night’s game?
1. 1
Burnley fans inside Turf Moor for the Championship fixture against Norwich City. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
2. 2
Burnley fans inside Turf Moor for the Championship fixture against Norwich City. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
3. 3
Burnley fans inside Turf Moor for the Championship fixture against Norwich City. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
4. 4
Burnley fans inside Turf Moor for the Championship fixture against Norwich City. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard