Pierre-Emerick Aubameyang's opener was followed by a Danny Welbeck double at the Emirates Stadium on Sunday, helping the hosts to a 3-2 victory.
The Saints, meanwhile, remain mired in relegation trouble as strikes from Shane Long and Charlie Austin proved insufficient to pick up a result from north London.
It was Arsenal's sixth consecutive win, but even more impressive is the Gunners' current form in front of goal.
Sunday's triple means that Arsenal have hit three goals or more in five successive home games for the first time since 1958-59, almost 60 years ago.
The game also marked yet another fruitless visit to north London for Southampton boss Mark Hughes.
Only Harry Redknapp against Manchester United, with 15 negative results at Old Trafford, is on a longer wait for an away win against an opponent in the competition