Marco Silva's Fulham Cottagers, who had lost only once in their previous seven home games in all competitions, are eighth in the league.
Gabriel, who also netted his debut goal against Fulham in 2020, put Arsenal on the scoreboard in the 21st minute with a header from inside a crowded six-yard box off Trossard's corner kick.
The Gunners had appeared to get on the board even earlier but Antonee Robinson's own goal was ruled offside by the VAR.
Trossard teed up Martinelli in the 26th minute when his arching cross dropped at the far post for an easy header, the Brazilian's 12th goal of the season. Only four Premier League players have scored more.
Seconds before halftime, Odegaard took two touches to control Trossard's cross before smashing the ball past Fulham -- and former Arsenal -- keeper Bernd Leno.
Trossard, who was signed by Arsenal in January, said he had no negative feelings about not scoring.
"Really happy with it, I always try to help the team with goals and assists and help the team going forward," the Belgian said. "Today, it went my way and I'm just really happy that we won."
Brazilian Gabriel Jesus earned a roar from Gunners fans when he entered the game in the 77th minute, his first action since a knee injury suffered at the World Cup in November.
"It's a massive boost, he's been out for a while now and we know what he's going to give to the team again, and we're all excited to have him back," Odegaard said. "Very happy for him and for the team."
Jesus nearly scored in the 85th but his shot from close range went straight to the keeper.
Fulham found some life midway through the second half, with a couple of excellent scoring chances, including a header by Aleksandar Mitrovic that clanged off the crossbar.