It was a sloppy start from Arsenal and Southampton took full advantage as some woeful defending from Shkodran Mustafi allowed Shane Long to poke home for 0-1 in the 17th minute.
Two quickfire goals from Pierre-Emerick Aubameyang and Danny Welbeck put the home side ahead going into the break.
Welbeck put the hosts ahead as he collected Alex Iwobi's slide-rule pass before cutting inside and seeing his shot deflect in off the heel of Maya Yoshida.
The game even ended on a fractious note, with Mohamed Elneny and Jack Stephens both sent off after a late scuffle.
Welbeck should have grabbed the lead for the home side five minutes later but he failed to convert from with the net gaping.
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Cech repelled firm drives from Pierre-Emile Hojbjerg and Wesley Hoedt but required assistance from Elneny to keep out a header from Stephens, the Egyptian midfielder - stationed on the back post for a corner - nodding the ball clear with his keeper beaten.
Yet they will return to the south coast with nothing to show for their efforts, Welbeck heading in the game's decisive fifth goal before tensions boiled over during added time.
- Arsenal have won six matches in a row in all competitions for the first time since May 2017 (also six). Long is not the most prolific but he showed a poacher's instinct in opening the scoring with his second goal of the Premier League campaign, and his willingness to run the channels was vital against opponents who dominated possession.
Goalscorer Charlie Austin echoed his manager's frustration.