The Gunners headed to Spain having lost their previous European match against Lens, a result that remains their only defeat of the season across all competitions.
A fairly dull first-half looked set to finish goalless as the fourth minutes of stoppage-time ticked away, but Arsenal's Brazilian duo up front had other ideas.
Gabriel Jesus held the ball up and produced a stunning turn to create the space, playing Gabriel Martinelli clean through on goal and he held his nerve to go round the goalkeeper and finish into an empty net.
Jesus then got a goal himself after the break, one his performance thoroughly deserved, and it was a strike to remember. He cut inside onto his right box as he jinked into the box, and curled a wonderful finish into the far corner to double the lead.
That two-goal advantage lasted only six minutes though, as Sevilla quickly got themselves back in it and woke the home fans up again. It came in frustrating fashion too from an Arsenal perspective, as Ivan Rakitic whipped a corner in and Nemanja Gudelj was allowed space to power a header beyond David Raya.
The hosts piled on the pressure late on, the ball regularly launched into the Arsenal box and the visitors looking nervy in their own box, but they just about held firm for a victory that leaves them in pole position at the halfway point of the group-stage.