McCarthy faltered under pressure from Eddie Nketiah following a back-pass, allowing the striker to intercept his attempted ball out slot into an unguarded net.
The win was sealed late on when Jack Stephens was sent off for fouling Pierre-Emerick Aubameyang as the last man and from the resulting free-kick substitute Joe Willock finished after Alexandre Lacazette’s free-kick struck the wall and his follow-up was parried.
It was timely boost for the Gunners, who have struggled with injuries and form since the restart, losing their two games prior to this.
The victory, though, was not undeserved. Prior to the goal, Nketiah had seen a close-range finish ruled out for offside and Aubameyang had crashed an angled effort against the bar.
Coming after such an impressive display in their first game back at Norwich, the result continues Southampton’s woeful inability to replicate their away form at St Mary’s.
This was their 10th loss at home this season – equalling the club record for a Premier League season, set back in 1993-94 when their were 42 games in a campaign.
With 11 points separating them and the bottom three it is very unlikely that they will get dragged into a relegation fight.
Arsenal’s win takes them back up to 10th but they still have a lot of work to do if they are to salvage something from this league season and qualify for Europe.
Small steps forward for Arsenal
Since the restart, the Gunners have lurched from one mini-crisis to the next – David Luiz’s calamitous display against Manchester City, injury problems galore, and a winning position thrown away at Brighton.
Two defeats from two games since the restart had already put paid to Arsenal’s already slim hopes of qualifying for the Champions League.
It also placed them in serious danger of recording their worst league finish since 1994-95 – the season in which George Graham was sacked and they ended up 12th.
That threat is far from over but what is just a third away win in 16 fixtures this season, coming from a much more assured performance, will bring at least a small injection of confidence and calm.
Goalkeeper Emiliano Martinez, in for the injured Bernd Leno, was solid, Granit Xhaka returned effectively in midfield and Nketiah and Aubameyang were typically lively in attack.
However, it would not be this current Arsenal without some shadows lurking in the background.
Full-back Kieran Tierney, who has been hampered by injury problems since joining the Gunners from Celtic last summer, limped out of the game in the second half.
Also, Matteo Guendouzi was left out of the squad entirely. While manager Mikel Arteta stated that his exclusion was down to “squad management”, he also did not entirely dismiss speculation that the Frenchman blotted his copybook by clashing with Neal Maupay at the end of the Brighton game on Saturday.
No home comforts for Saints
Southampton’s Ralph Hassenhuttl is an animated manager at the best of times but spent much of Thursday’s game prowling the touchline with a frustrated look and sweat on his brow.
Having handed the Austrian a new four-year deal at the start of this month, the Saints recognise a man with a plan and a project worth pursuing.
His first job, though, is to rectify the disparity between their away and home results.
Away from St Mary’s they appear unburdened, pressing effectively and counter-attacking with menace, but back on the south coast they struggle to exert themselves, even without the pressure of fans in the stands.
Their display was not completely without merit but attacks tended to yield half-chances from long range for James Ward-Prowse, Stuart Armstrong and Nathan Redmond as opposed to the kind of clear-cut ones that have enabled the likes of Danny Ings to thrive this campaign.
Ings’ one big chance of the game came in the final quarter when he was released behind the defence by a long ball forward, but his drive was parried well by Martinez.
It may get worse before it gets better, though. Manchester City are the next visitors to St Mary’s.