Goals late in the first half from player of the season Bradley Johnson and Nathan Redmond put the Canaries in control, with Graham Dorrans making it three near the end of the match.
Matt Smith pulled a goal back for Fulham with seven minutes to go but Johnson doubled his tally to make it 4-1 before he got on the scoresheet for a third time, only on this occasion it was through an own goal.
The win saw Norwich finish third – and set up a mouthwatering play-off semi-final encounter with East Anglian neighbours Ipswich.
With a place in the play-offs already assured there was a lack of intensity in Norwich’s early play and they had to wait until the 17th minute for their first clear sight of goal.
A sweeping move down the right ended with Johnson taking aim from just inside the box but a good chance went begging as he dragged his shot wide.
Fulham, who went into the game with a 16-match unbeaten run against Norwich stretching back to 1986, were also struggling to create chances as passes went astray on a regular basis.
A disjointed, scrappy match was crying out for a goal and it arrived out of the blue in the 36th minute when Wes Hoolahan picked out Gary Hooper’s well-timed run behind the visitors’ defence. The striker got to the byline and had all the time in the world to pick out an unmarked Johnson who gleefully slotted home his 14th of the season.
Three minutes later it was 2-0 as more poor Fulham defending was punished. This time the visitors were guilty of standing back as Redmond moved into the box and the England Under-21 star curled a superb shot into the far corner to double Norwich’s advantage.
Fulham should have pulled one back just before the break when Hugo Rodallega broke clean through but with just John Ruddy to beat he lobbed carelessly over the bar.
The Cottagers’ front man did a lot better just after the break as he got in a shot on goal from a tight angle, but an alert Ruddy was well placed to save.
It was a far better game now and the lively Redmond forced Marcus Bettinelli into his first genuine save of the game when he let fly from 20 yards.
The flow of the game was not helped by four substitutions, two for each side, but Norwich continued to have the better of it, with Bettinelli having to be alert to grab a Gary O’Neil free-kick that was heading into the bottom corner
Fulham were also much better than they were in the first half and nearly pulled one back 15 minutes from time when Shaun Hutchinson’s goal-bound effort was blocked by O’Neil
Hooper then saw his deflected shot on the turn clip the upright as the Canaries attempted to finish their regular season with a flourish.
City duly made it 3-0 in the 81st minute when Redmond danced into the area from the left before squaring to Dorrans for the simplest of finishes but Fulham got a deserved consolation almost immediately.
A poor defensive header fell nicely for substitute Smith who volleyed clinically past Ruddy.
There was still time for Johnson to make it 4-1 with a powerful low strike from distance – and then head an inswinging free-kick into his own net to complete the scoring.