Alexandre Lacazette and Henrikh Mkhitaryan both scored inside 20 minutes, with the former failing to take further advantage of a disjointed Southampton side.
The defeat leaves Southampton, who looked nowhere near the side that won at St Mary’s, a single point adrift of relegation rivals Cardiff City and safety as they enter a difficult run of games ahead, including Manchester United and Tottenham.
Lacazette back-heeled a pass from Mkhitaryan in for the game’s opening goal before Alex Iwobi set up the Armenian midfielder 11 minutes later thanks in part to a goalkeeping error by Angus Gunn.
Southampton mustered just four shots on target, but never truly put Arsenal under any sustained pressure.
Arsenal: Leno, Kolasinac, Papastathopoulos, Mustafi, Lichtsteiner (Koscielny 56), Xhaka, Torreira, Iwobi (Aubameyang 75), Ramsey (Ozil 63), Mkhitaryan, Lacazette.
Unused subs: Cech (GK), Monreal, Suarez, Guendouzi.
Goals: Lacazette (6), Mkhitaryan (17).
Southampton: Gunn, Vestergaard, Stephens (Austin 46), Bednarek, Targett, Valery, Ward-Prowse, Romeu, Hojbjerg, Armstrong (Obafemi 46 (Elyounoussi 65)), Redmond.
Unused subs: McCarthy, Yoshida, Bertrand, Slattery.