The Gunners responded well to their 5-1 mauling on Merseyside at the hands of Liverpool on Sunday (AEDT), with the home victory pushing them to within two points of fourth-placed Chelsea in the Premier League table.
Yet Fulham did not make life easy for its host, Ryan Sessegnon missing two excellent opportunities before Granit Xhaka opened the scoring in the 25th minute.
Alexandre Lacazette doubled the lead but Claudio Ranieri's side hit back through Aboubakar Kamara after 69 minutes, forcing Arsenal to weather a shaky period before easing clear with two late goals.
"We wanted to win and this result will give confidence," Emery said. "We continued to push and create chances and we can be happy.
"It is normal for the fans to have some doubt at 2-1, but the team continued to do their work and played our planned game.
"I thought we deserved the scoreline. We scored with different players and we can continue to build our identity with the players."
Aaron Ramsey converted a rebound after Pierre-Emerick Aubameyang had hit the post to make it 3-1, while the latter rounded out the scoring with a deflected strike to take his tally in the league this season to 14.
Midfielder Xhaka was pleased to help his side return to winning ways, particularly with London derbies against West Ham and Chelsea to come after an FA Cup third-round tie at Blackpool this weekend.
"After a bad game against Liverpool, we want to show a good game and to improve," the Switzerland international said.
"Fulham have a new coach and a good team. We were a bit nervous at 2-1, but 4-1 makes us happy.
"We can learn a lot from the game against Liverpool - they are a good team this year - but we have West Ham away and then Chelsea at home which is a tough schedule."