Southampton looked bad in the first half, but then recovered just a little bit in the second half, as they did put a few chances on goal.
The match proved that these are two clubs heading in two different directions with Arsenal potentially challenging for a title while the Saints will be struggling to stay in the top flight for a second season.
Here are five things we learned from Saturday's Arsenal win.
After Robin van Persie left Arsenal for Manchester United in August, there were many concerns about the Gunners' attack.
Those concerns have all but gone away now after Saturday's win.
In the 6-1 win, Gervinho scored twice while both Lukas Podolski and Theo Walcott scored one goal each.
Other attacking players such as Santi Cazorla, Alex Oxlade-Chamberlain and Aaron Ramsey also contributed to a steady flow of scoring chances throughout the match.
However, the one thing that critics of the club may hold against the Gunners' attack is that they did this against lowly Southampton.
Next Sunday's match with Manchester City will be a test for the men up front for Arsene Wenger's club to prove they have moved on after van Persie.
There were very few players who did not perform well on Saturday, but the ones who did stood out.
The one who stood out most was Wojciech Szczesny.
Szczesny was at fault for the only Southampton goal, which came at the end of the first half.
The Poland international was unable to hold on to a save, and with Danny Fox waiting around for a rebound, the Saints defender took advantage of the mistake and scored.
With Vito Mannone lurking in the shadows of Szczesny at the goalkeeper position, the current No. 1 keeper for Arsenal needs to play better than he did Saturday to keep his job.
Nigel Adkins has led Southampton to two consecutive promotions, going from League One to the Premier League in two seasons, but his luck may be running out.
After four matches this season, the Saints are the only club to not earn a point.
On Saturday, the Saints looked more like a Championship side instead of an EPL side. Two ugly goals were given up by Jos Hooiveld and Nathaniel Clyne in the first half.
If Adkins' club continues playing like they did on Saturday, Adkins easily could be sacked by the Saints front office regardless of what he has achieved the past two seasons.
After taking care of Liverpool in their last EPL match and winning easily on Saturday, Arsenal have proven that their slow start was not a representation of how the season will go.
As the Gunners head into Champions League play on Tuesday, it looks like the squad is ready for the European stage.
On Saturday, the Gunners played like a top-four EPL side, and if they continue to play that way, Group B in Europe's top club competition should not be a problem at all.
The Gunners start Group B play on Tuesday as they travel to France to take on Montpellier.
After two spirited performances against Manchester City and Manchester United, Southampton fell flat during their trip to the Emirates Stadium on Saturday.
The Saints have no points from their first four matches, and in their one match against a relegation contender, Wigan, they lost 2-0.
Next up on the schedule is Aston Villa at home, which could be a turning point in the Saints' season if they win.
But if they lose to Villa next week, it could turn into a very long season, as the newly promoted club may be headed right back to the Championship.
Editor's note: This slideshow originally contained another slide involving a suggestion about Bacary Sagna that was incorrectly based on him playing the left-back position. That slide has been removed to foster factual accuracy.