Emery's side turned on the style on the banks of the River Thames, romping to its biggest win of the season as the resurgent Gunners moved into the Premier League's top four, AFP reported.
Alexandre Lacazette sparked Arsenal's power surge at Craven Cottage, with his superb second-half strike restoring the lead after Andre Schurrle had cancelled out his opener.
Aaron Ramsey's audacious back-heeled goal put Arsenal in complete control to cap a stunning move that recalled the club's finest days under Emery's predecessor Arsene Wenger.
Pierre-Emerick Aubameyang netted twice in the closing stages as Arsenal won six consecutive league matches within a single campaign for the first time since 2016.
It was a significant statement of intent from a team widely written off ahead of Emery's first season in charge.
"Our performance over the 90 minutes was very important. We worked very hard in the second half to get this result with our momentum on the pitch," Emery said.
"I believe in us, we believe in our process but also we must keep taking confidence. I think we are in the first part of the war.
"It is very difficult but we must prepare, continue improving and show big commitment."
Emery was expected to need a long period to revive Arsenal after the depressing final years of the Wenger era.
But the former Paris Saint-Germain boss has helped Arsenal quickly rediscover its verve and struggling Fulham had no answer to its enterprising display.
No wonder jubilant Gunners crammed into one corner of Craven Cottage celebrated the goal with chants of "We've got our Arsenal back".
That unity between fans and players was badly missing as supporters staged protests against Wenger last season.
"You need to feel together with the supporters and the players. This spirit and mentality is very important for us," Emery said.
"To show our quality and work, then together we can be happy like today. We need them to support us. The players feel that.
"We are happy but also calm because we know each match is difficult. We are going to continue working."
While Arsenal is improved, it has been aided by a soft fixture list in recent weeks and even Emery demurred when asked if his team is now a title contender.
"We lost the first two matches against Manchester City and Chelsea. We were calm then and we need to be the same way in our mentality when we are winning," he said.
"I don't want to look back. Every match is different. We have a better position in the table for our objections, but we have to be calm."