The game exploded into action as early as the third minute as the hosts opened the scoring in emphatic fashion.
Luciano Vietto laid the ball off to Jean Michael Seri at the top of the area, the Ivory Coast international taking a touch and rifling a ferocious effort into the top corner of the net.
Burnley were then handed a major setback when Johann Berg Gudmundsson had to be substituted eight minutes later with what appeared to be a hamstring injury.
The latter stages of the first half saw a flurry of goals as Aleksandar Mitrovic headed home in the 36th and 38th minutes of the match to give the hosts a two-goal cushion.
The second half continued much in the same vein, though it was not quite as eventful as the first, but Fulham nonetheless managed to put the game out of reach with a fourth goal on 83 minutes.
The result means that Fulham have their first points of the season and move out of the bottom three while Burnley, with just one draw so far this season, slip into the dropzone.
FULHAM (4-3-3): Bettinelli; Fosu-Mensah, Odoi, Le Marchand, Bryan (Chambers 71'); McDonald, Cairney (Anguissa 78'), Seri; Vietto, Mitrovic, Schurrle (Sessegnon 88')
BURNLEY (4-4-1-1): Hart; Lowton, Mee, Tarkowski, Ward (Barnes 66'); Lennon, Cork, Westwood, Gudmundsson (Taylor 19'); Hendrick; Wood (Vokes 66')