Early strikes from Alexandre Lacazette and Henrikh Mkhitaryan were enough to secure the three points and leave Saints in the bottom three.
Southampton created enough chances to have at least got on the scoresheet but it was at the back where they were again suspect and they remain 18th and a point from safety after leaving the Emirates Stadium empty-handed.
Arsenal had a great early chance as Nathan Redmond broke the offside trap and ran through on goal, only for Bernd Leno to rush off his line and block the shot.
Arsenal went straight down the other end and took a sixth-minute lead as Lacazette coolly turned home a wayward Mkhitaryan volley after calls for a foul on Lucas Torreira had fallen on deaf ears.
Southampton responded well to their early setback and had two decent opportunities to level as Stuart Armstrong’s header was blocked by Sead Kolasinac before Matt Targett’s strike was palmed away by Leno.
Once again, Ralph Hasenhuttl’s men were made to pay almost instantly as Jack Stephens miscued a backpass with goalkeeper Angus Gunn closed down by Alex Iwobi. His deflected pass found a way through to Mkhitaryan, who made no mistake with an unerring finish to double the lead.
Hasenhuttl made two changes at the interval as both Charlie Austin and Michael Obafemi came on – but it was James Ward-Prowse who came close to pulling one back after Xhaka had gifted him the ball on the edge of the box.
Aubameyang should have done better when played in behind but opted to cross the ball, Jannik Vestergaard’s deflection almost leading to an own goal but for some good work from Gunn.