Leandro Trossard scored his second goal in the Champions League this season to put Arsenal ahead
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.
-- Courtesy of BBC Sport