Russell Martin's winless crop were on course for one of the upsets of the season when Cameron Archer opened the scoring in the second half, but the Saints eventually succumbed to incessant Gunners pressure, as Kai Havertz, Gabriel Martinelli and Bukayo Saka completed a statement turnaround.
Reuniting with former number one goalkeeper Aaron Ramsdale, Arsenal may have expected to pepper the Englishman's goal with shot after shot, and so it proved inside the opening 20 minutes.
However, after withstanding early intense pressure from the Gunners, Southampton began to weather the storm with ease, happily conceding possession to an Arsenal side who lacked ingenuity in the final third.
Raheem Sterling - making his maiden Premier League start for Arsenal - was doing his bit to make things happen, but Southampton's defence was unwavering as they got to the break with their clean sheet intact.
Things got even better for the Saints when Archer found the far corner early in the second half, but going behind was the kick that Arsenal needed to finally find a touch of ruthlessness, and Ramsdale was powerless from thereon in.
A clinical Havertz finish, close-range Martinelli volley and low strike from Saka - who had set up both of his teammates' goals - ensured that Arsenal would be celebrating their 400th Premier League home win, becoming just the second team to hit that landmark after Manchester City.
As the Gunners remain third behind Manchester City and Liverpool, Southampton are only being kept off the foot of the table by Wolverhampton Wanderers and remain without a single top-flight win in 2024-25, leaving Martin's job clouded in further uncertainty.
ARSENAL VS. SOUTHAMPTON HIGHLIGHTS
Cameron Archer goal vs. Arsenal (54th min, Arsenal 0-1 Southampton)
All that Arsenal pressure, all of Southampton's dogged defending, and yet the upset of the season so far could be on the cards at the Emirates!
The hosts cry for a foul on Sterling - pleas that fall on deaf ears - and Southampton break forward before Archer finds the far corner with panache, sending the away end into delirium.
Kai Havertz goal vs. Southampton (58th min, Arsenal 1-1 Southampton)
Well, it turns out a Southampton goal was just the catalyst that Arsenal needed to finally break down this stubborn Saints defence!
The Gunners are only behind for four whole minutes, as Saka intercepts a shocking pass from Flynn Downes and feeds Havertz, who sets himself on his left foot and fires a clinical strike in off the post. Game on!
Gabriel Martinelli goal vs. Southampton (68th min, Arsenal 2-1 Southampton)
Arteta's substitutions have the desired effect!
Martinelli - who has only been on the pitch for a matter of minutes - scores for the second home game running in the Premier League, volleying in at the back stick from Saka's second assist of the afternoon, and what a cross it was.
There is a lengthy VAR check for a possible offside, but Martinelli's goal eventually gets the thumbs-up from Stockley Park, and Arsenal lead for the first time this afternoon!
Bukayo Saka goal vs. Southampton (88th min, Arsenal 3-1 Southampton)
Game, set, Saka.
After providing his sixth and seventh assists of the season for Arsenal's first two goals, the England sensation makes sure of the points with one of his own. Arsenal break quickly through Leandro Trossard, who is stopped by Yukinari Sugawara, but the right-back's heavy touch falls for Saka to find the far corner.
MAN OF THE MATCH - BUKAYO SAKA
Last weekend, Bukayo Saka thought that he had become the first Premier League player to set up a goal in each of a team's first six games of the season, only for an own-goal ruling to deny him that record.
However, the playmaking master - who is filling Martin Odegaard's creative boots expertly, by the way - helped himself to another two assists this afternoon, firstly stepping in to intercept Downes's poor pass before a sublime delivery to Martinelli at the back post. A late goal of his own was just reward for his proficient playmaking.
Saka has now provided more Premier League assists for Arsenal than Robert Pires. He is 23 years old.
ARSENAL VS. SOUTHAMPTON MATCH STATS
Possession: Arsenal 59%-41% Southampton
Shots: Arsenal 29-8 Southampton
Shots on target: Arsenal 6-2 Southampton
Corners: Arsenal 13-1 Southampton
Fouls: Arsenal 10-9 Southampton
BEST STATS
WHAT NEXT?
Following the international break, Arsenal coincidentally head south to face Bournemouth on October 19, three days before they resume their Champions League campaign against Shakhtar Donetsk.
Meanwhile, Southampton - who have a massive call to make on Martin's future over the next two weeks - return to action at home to fellow newly-promoted side Leicester City in a fortnight's time.