The Saints were happy to sit back for large parts of the game but the Gunners finally got the goal their possession deserved at the death.
It was another frustrating performance from Arsène Wenger's team, but what did we learn from their display on the South Coast?
Gunners continue to struggle on the road
If you needed any indication of how poor Arsenal have been away from home this season then the fact they've only won twice tells you all you need to know.
The Gunners can't seem to string together any consistency away from home and if it wasn't for a late Alexis Sánchez penalty at Burnley it would only be one win in eight games away from the Emirates.
In those eight games they have meanwhile only scored eight goals, five of which came in the rout at Everton, a victory that stands as their only convincing win away from home all season.
At St Mary's on Saturday the game had a similar feel to it, only for Giroud to dig them out of a hole with two minutes to go.
Arsenal may be better off without Sánchez
There is no doubting Sánchez's quality, but this season his form has perhaps left Arsenal rueing their decision to not sell him to Manchester City.
Instead they could be losing him for a much lesser fee or even on a free depending if he leaves in January or when his contract ends.
He may have got the assist for the goal but his overall performance was poor. That has been the case on a number of occasions this season though.
Most of the criticism gets aimed at perennial scapegoat Mesut Özil when Arsenal struggle to create but Sánchez's displays also deserve to be under the microscope.
In Arsenal's last two Premier League games Sánchez has a pass completion rate of just 69% and has given the ball away a staggering 66 times.
For a player of his quality those are alarming statistics, but it may not come as a surprise to Gunners fans who saw similar sort of displays last season.
However in 2016/17 he was scoring goals at will to make up for it, something which is in stark comparison to his current campaign so far.
Giroud continues to be an asset
If Giroud was close to leaving for Everton in the summer then Arsenal will be mightily relieved that he chose to stay in North London. He has appeared off the bench 13 times and is yet to start a single league game but that could be about to change after his contributions in recent matches.
He scored two after replacing Alexandre Lacazette in the Gunners' 5-0 win over Huddersfield Town and impressed again when he came off the bench here against Southampton.
His header was impressive, but who is to doubt the Frenchman's prowess in the air? It was a perfectly-placed header and it was typical that he was there to pick up the pieces from another disappointing Arsenal performance.
Since the start of last season Giroud's strikes have earned the club seven points that they wouldn't have had if he hadn't have scored. It's a record that may have slipped under the radar, but it shows just how undervalued Giroud is.
Defensive frailties are still there
The strange thing about Arsenal's recent defensive displays is that they have come out of nowhere. It looked as though they had finally addressed their issues; Shkodran Mustafi had six Premier League clean sheets from seven games but in the last two matches Arsenal's old nemesis has returned in the form of their defence.
In the game with Manchester United last week they were all over the place at the back early on and it was the same story at Southampton as they found themselves a goal down inside three minutes.
The Gunners have a habit of making life hard for themselves and their fragility appears to have returned in the past couple of weeks.
It may be a case that Wenger looks to revert back to four at the back, a system he operated with in mid-week against BATE Borisov in the Europa League. That was able to free up an attack that on occasions this season has been rather off the boil, particularly against Southampton on Sunday.
Arsenal are already out of the title race but the aim for them this season was surely a spot back among Europe's elite in the Champions League. The draw did see them move back ahead of Spurs, but they have to improve if they want to continue to challenge for a top four spot.