The Spanish side have won the UEFA Cup in the last two seasons but Juande Ramos' team were well-beaten by a Gunners outfit that looked supremely confident after making an excellent start to the campaign.
Arsene Wenger's side started brightly but it was Seville that created the first opening of the game in the sixth minute when a fizzing long-range Jesus Navas effort was only just too high.
Seven minutes later the Gunners created two good chances in quick succession. Visiting goalkeeping Andres Palop made a hash of saving Robin van Persie's rasping effort although he was able to bundle the ball away for a corner.
He then parried Mathieu Flamini's shot and was just able to grab the ball at the second attempt as Emmanuel Adebayor tried to slot home the opener.
The Gunners seemed to be running out of ideas when they fortuitously took the lead in the 27th minute when the in-form Cesc Fabregas' ambitious shot deflected off Julien Escude's chest and beat the unfortunate Palop.
It was the young Spanish midfielder's fifth goal in his last five games.
Seville lost their way after the opening goal and it was Wenger's side that looked more likely to add to their lead before the interval.
In the 34th minute Kolo Toure got his head to Tomas Rosicky's excellent corner, but his effort flew wide before Adebayor used his strength and pace to get past Julian Fazio but the Togo man's finish was poor as his shot flashed well wide.
Another intricate Gunners passing move ended with Flamini's shot from the edge of the area being easily gathered by Palop, while at the other end former Spurs star Freddie Kanoute's stinging effort was clawed away by Flamini for a corner.
On the stroke of half-time, Kanoute beat the offside trap but was just unable to get his head on to Christian Poulsen's cross and the ball rolled narrowly wide.
The game was effectively over just before the hour mark. Fabregas curled in a free-kick that Bacary Sagna flicked on with his head and van Persie lashed the ball home from close range.
Seville tried to hit back and Kanoute's trickery allowed Daniel Alves to find some space on the right but the Chelsea target's pass across the area could not find a team-mate.
It was almost 3-0 in the 70th minute when Adebayor's excellent header from Sagna's pinpoint cross was inches wide with Palop beaten.
At the other end, Poulsen had a shot blocked on the edge of the area after an intricate move involving Kanoute and Alves before Kanoute's half-volley from just inside the area flew narrowly wide.
However, Arsenal confirmed their dominance with a third goal in stoppage time. Alex Hleb and Fabregas set up substitute Eduardo who side-footed the ball home from close range.