After losing at the same stadium to the same opponents on Saturday, the Gunners stretched their unbeaten league run to six games.
It didn't go completely to plan, though, as Stuart Armstrong opened the scoring for Southampton after just three minutes as he volleyed home from a corner.
But the visitors were soon back on level terms when Granit Xhaka threaded a pass-through for Nicolas Pepe to control and slot home.
Bukayo Saka then completed the turnaround before the half-time break, racing through to round Alex McCarthy and shoot into an empty net.
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Alexandre Lacazette then sealed the victory for Arsenal, tapping home Saka's cross from close range after a superb switch of play by Cedric Soares.