Trossard, who started as number nine with Gabriel Jesus and Eddie Nketiah both injured, swept the Gunners in front in the 29th minute.
Saka clinched the three points in the 64th minute, racing away from the defence before slotting home.
Arsenal top Group B on nine points from four games, while Sevilla are bottom of the table.
The Spanish side, who won the Europa League last season, are still looking for their first win in this Champions League campaign.
They were comprehensively outplayed by the hosts, who took a deserved lead when Trossard finished Saka’s low cross after the England winger was set away by Jorginho’s fine through-ball.
Saka turned from provider to finisher with a composed second goal, having been played through by Gabriel Martinelli.
“I’m really happy with the performance from the team,” Arsenal manager Mikel Arteta told TNT Sports.
“They showed aggression and commitment. Even when we lost the ball we were incredibly good to get it back. It’s hard in Europe to control it how we did.”
The game ended on a concerning note for Arsenal as Saka limped off with five minutes left after twisting his ankle, however Arteta said it was only a “knock”.
PSV’s 1-0 victory over Lens denied Arsenal the chance to clinch a place in the last 16 with two matches to spare.
But Arteta’s men will qualify with a point from either of their final two group matches against Lens or PSV.
Trossard fronts up as Gunners end wobble
Following a strong start to the season, the past week has been testing for Arsenal. Back-to-back losses included the controversial 1-0 defeat at Newcastle, after which Arteta said the refereeing decision to allow the winner was “embarrassing” and a “disgrace”.
The Gunners have also had to deal with mounting injuries – Nketiah missed out with an ankle knock to join Jesus on the sidelines, leaving Trossard to lead the line. Captain Martin Odegaard was also absent again.
Trossard, however, eased worries about Arsenal’s forward strength with his goal and performance, and is ready to play the role again if needed.
“When I saw Jorginho on the ball I knew he would put it in behind for Saka,” the Belgian said of his opener. “It’s a great team goal and it set us up for the rest of the game.
“My biggest quality is that I can go on both feet. It doesn’t really matter for me if I play wide or inside. I have played in multiple positions in my career and it has helped me a lot.”
Injuries left Arsenal without a full bench, and there were also questions about the form of some senior players who did feature.
Kai Havertz has been a target for supporter ire – and he spurned a simple chance to hand Arsenal the lead inside a minute, heading a corner wide when unmarked five yards out.
The German also lacked conviction shortly after half-time when fed by Saka on the edge of the area following a counter-attack, but his shot was blocked.
Havertz came closer on 55 minutes when curling a fierce 18-yard effort just wide.
What Arteta needed was a straightforward night against out-of-form opposition – and against a pliant Sevilla side, he got it.
