Fulham gave Arsenal an early scare when Aboubakar Kamara forced a smart save from Bernd Leno.
Alexandre Lacazette opened the scoring on eight minutes, tapping in after Marek Rodak had pushed Willian’s shot to him.
In so doing, the forward became the first player to score the opening goal of a Premier League season more than once.
Three minutes after half-time Willian, having also struck a post with a first-half free-kick, delivered a corner that was headed in by another debutant, Gabriel.
Pierre-Emerick Aubameyang collected Willian’s long pass to superbly curl in Arsenal’s third on 57 minutes.
It gave Arsenal their biggest away league win since beating Fulham 5-1 in October 2018.
Budweiser King of the Match Willian
Fulham: 19 Sep v Leeds (A)
Arsenal: 19 Sep v West Ham (H)