Manager Alex Neil had gone into the game under some pressure after seeing his side suffer five consecutive league defeats to slip out of the top six.
But the Canaries got their faltering promotion challenge back on track against a poor Bees side, with an early own goal setting them on way before Graham Dorrans, Robbie Brady, Nelson Oliveira and Alex Pritchard all got in on the act.
It was Norwich’s biggest win of the season – while for Brentford it was a fourth straight defeat after what had been an encouraging start to the campaign.
City started the game on the front foot and got their noses in front after just six minutes when Brady’s delicious cross from the left went off off defender John Egan, with Jacob Murphy in close attendance.
Looking anything but a side on a terrible run, the home side then doubled their advantage 10 minutes later after Harlee Dean had brought down the quick-silver Murphy in the box.
Dorrans’ penalty was saved by Daniel Bentley, but the rebound fell kindly for the Scottish midfielder to convert second time around.
Neil’s men were unable to maintain their early intensity but fortunately for them Brentford rarely threatened their goal and the points were effectively wrapped up on the hour mark.
A superb ball from a central area from Pritchard picked out Brady’s run and the Republic of Ireland international produced a finish to match to make it 3-0.
Norwich continued to dominate and stretched their lead in the 79th minute when Oliveira was allowed time and space in the area to trun and thump the ball home.
The icing on the cake was provided in injury time as Pritchard finally got the goal he deserved after linking up with substitute Josh Murphy before sliding the ball home.