The siege on the Southampton net began in the 11th minute as the Saints conceded an own goal off of defender Jos Hooiveld.
The ball deflected off Hooiveld after goalkeeper Kelvin Davis saved a shot from Arsenal defender Kieran Gibbs.
It was 20 minutes until the Gunners scored their second goal of the match, which came in the 31st minute, thanks to a Lukas Podolski free-kick.
The free-kick was set up by a foul committed by Steven Davis, who took down Francis Coquelin outside the penalty area.
Podolski made the visitors pay for their mistake when his free-kick sailed into the left side of the net past Davis.
The next Arsenal player to join the scoring party was Gervinho.
The Ivorian snuck past the Saints' defense and, after he received a beautiful chip pass from Mikel Arteta, he scored in the 35th minute.
Three minutes after Gervinho found the back of the net, the Gunners were on the scoresheet again, as Southampton scored their second own goal of the match.
Just like the first own goal, the ball came off of a Southampton defender after a cross from Gibbs.
This time, the unfortunate defender was Nathaniel Clyne.
Right before the end of the first half, Arsenal committed one of their few mistakes of the match.
Wojciech Szczęsny could not hold on to a save and Danny Fox was waiting to poach. He scored the Saints' only goal of the day in the 45th minute.
The second half did not bring as much excitement as the first half did, but there were still a good amount of goals.
Gervinho netted his second goal of the match in the 71st minute after a shot by substitute Aaron Ramsey was not cleared properly.
The Gunners' final goal of the match came in the 88th minute as Theo Walcott scored on a rebound from a Thomas Vermaelen shot.
The dominant performance was just what the Gunners needed as they head into a stretch of big games in the next week.
Before travelling to the Etihad Stadium to face Manchester City on Sunday, the Gunners have to make the trip to France to take on Ligue 1 champions Montpellier on Tuesday in the UEFA Champions League.
As for Southampton, they are still looking for their first points of the 2012-13 campaign and will look to earn them on Saturday as they host Aston Villa at St. Mary's Stadium.