Pierre-Emerick Aubameyang and Aaron Ramsey then came off the bench to finish off the scoring, with the former scoring twice and setting up Ramsey for his goal.
Aubameyang sealed the victory in style, collecting Bellerin's cross and firing left-footed beyond Bettinelli on the turn, before striding onto Ramsey's pass and drilling into the bottom-left corner in injury time.
It was Arsenal who nearly regained the lead less than three minutes into the second half but Bettinelli pulled off a great save to deny Bellerin from the edge of the box.
After losing his first two matches - to champions Manchester City and Chelsea - the new boss has overseen a run of nine wins in a row in all competitions. The Gunners faced a decent Fulham side in a Premier League clash.
Unai Emery's side came out guns blazing after the break, with Hector Bellerin coming close to putting them back in front in the third minute of the half. It's one of the best team goals we've seen in a long, long time, and the skill moves pulled off during it - three to be exact - make it that much better.
Substitute Pierre-Emerick Aubameyang got in on the action, grabbing two goals in a memorable 30-minute cameo.
There are fears that Arsenal might lose star player Aaron Ramsey for free, without cashing in on him after they were unable to tie him down with a deal.
[I was pleased] not only with the first XI but with the substitutes.
The Germany worldwide split the two Arsenal centre-backs and his deft lob from Vietto's slide-rule pass deservedly saw Fulham draw level just before the interval.
Emery said, "Our performance over the 90 minutes was very important; to be together and with our performance we found each moment and each player". Today we are happy but we're going to continue going about our process with humility.
"I want to give them and to show them we are improving with our quality, with our mentality and above all with commitment we had here today". I think we are in the first competition in the war.