The game got off to an explosive start, with Alexis Sanchez curling a free-kick into the top corner from 25 yards, with Saints’ goalkeeper Fraser Forster beaten all ends up.
However, the Gunners’ lead only lasted six minutes, as Tomas Rosicky conceded a penalty after bringing down Saido Mane in the box.
Dusan Tadic converted, delaying his kick and calmly slotting the ball down the centre of debutant David Ospina’s goal.
And five minutes before the break Nathaniel Clyne grabbed what proved to be the winner, firing a thunderbolt in from distance that was hit with such ferocity that Ospina could not keep it out.
The Gunners threw everything at the Saints after the interval, but they couldn’t find a way through a determined backline, and Southampton continued their fine start to the season with yet another impressive win, while Arsene Wenger’s men crashed out on their own turf.
The Frenchman made 10 changes for this match, including giving injury-plagued Abou Diaby his first start in 18 months.
The only survivor from the league win at Aston Villa was Calum Chambers, facing the club he left in the summer as part of a back four with just 54 Arsenal appearances between them – the majority by Francis Coquelin, playing out-of-position at left-back.
That inexperience showed after nine minutes, when Ospina was forced to smother a Davis attempt after he was all too easily put through by Tadic’s ball over the top.
Arsenal’s first noteworthy attack soon followed but Rosicky directed a tame header at Forster, who was not so lucky the next time the hosts had an attempt.
Showing just why the Gunners forked out so much for him, marquee summer addition Sanchez dusted himself off after a foul to strike an exquisite 25-yard free-kick into the top-left hand corner – a strike so good Forster barely moved in the Saints goal.
It was a wondrous effort but one that only had the Gunners ahead for six minutes. Mane’s quick feet drew a penalty from Rosicky, with Tadic keeping his cool amidst jeers from the home fans to roll the spot-kick straight down the middle.
Saints soon returned to the attack with Mane hitting wide under pressure and Pelle clipping the woodwork with a first-time strike from a Tadic pass.
Arsenal were struggling to create clear-cut chances and Saints turned the match on its head with a fantastic long-distance effort of their own.
Tadic’s corner from the left was only cleared as far as Clyne, who took a touch before hitting fizzing 30-yard effort that Ospina could not cope with.
It was a wonderful goal that sent the visiting supporters into raptures and put Saints ahead at the break, which ended with Forster having to deny a close-range Lukas Podolski effort.
Saints returned strongly after half-time as Ospina was forced into a superb save low to his right to stop Davis ending a wonderful team move, involving teenager Matt Targett, Mane and Tadic.
Florin Gardos, making his full debut, headed over as Saints looked to put the match out of reach, which they would have done had Ospina not denied a low, powerful Tadic free-kick.
Arsenal upped the ante as the match entered the final 20 minutes, with Joel Campbell having a soft penalty claim rightly rejected before Forster made a crucial stop to deny Sanchez.
The Chile international failed to beat the wall with a free-kick as the clock wound down, with Jose Fonte and Gardos doing brilliantly at the heart of defence to keep Arsenal at bay as Pelle and substitute Shane Long came close at the other end.