Jordy Clasie netted the opener early in the first half to send Southampton on their way.
Ryan Bertrand doubled the Saints' advantage before the end of the first half as Arsene Wenger felt the strain of making ten changes to his side.
The home side tried to battle their way back into the game but couldn't spark a revival.
Southampton await the result of the semi final draw.
Saints shock Arsenal early
It only took 13 minutes for Southampton to take the lead and it was very much against the run of play. Bertrand crossed low and when the ball dropped to Clasie, the Dutchman thrashed the ball past Emiliano Martinez.
Fraser Forster then nearly gifted Arsenal a good chance to equalise when he appeared to fumble the ball over the line of his penalty area. The referee disagreed.
The Saints continued to pile the pressure on, as Shane Long broke past the Arsenal backline before being surrounded by red shirts.
The away side made their dominance count before the half was over as Sofiane Boufal slid the ball inside and Bertrand neatly finished to double Southampton's lead.
It got worse for Wenger's men soon after as Mohamed Elneny had to be taken off before the interval.
Southampton see it through
Arsenal had the first shot on target in the second half as Lucas Perez hit a tame effort at Forster.
Another chance came for Arsenal when the ball was crossed in by Jenkinson, who found Ramsey unmarked in the box, but the Welshman's shot looped into the arms of Forster.
However, it didn't take long for Claude Puel's side to get back in control of the game as the second half went on. Boufal saw his first effort of the second period fly just past the post.
Southampton nearly sealed the tie in the 54th minute as Sam Mcqueen and Cuco Martina linked down the right but Long couldn't get his shot away once the ball was in the box.
Arsenal kept trying in vein but couldn't create a clear-cut chance. Aaron Ramsey, Alex Oxlade-Chamberlain and Perez all had efforts off target as the game progressed.
The hosts continued to look for a way back into the game but couldn't get the better of Southampton's resilient defence.
Josh Sims, who impressed on his debut, nearly grabbed Soutampton's third with five minutes remaining. Pierre-Emile Hojbjerg also nearly capitalised on an Arsenal error to seal the tie in added time.
What it means
It is the second time Arsenal have been beaten by Southampton in the last 12 months.
The Gunners will now look to continue their success in the cups when the FA Cup starts again in the coming months.