Goals from Jordy Clasie – his first for the club – and Ryan Bertrand secured victory for a Southampton side which inflicted a first defeat on the Gunners since the opening day of the season.
Claude Puel’s side got off to the perfect start when Jordy Clasie fired into the top corner in the 13th minute.
Arsenal pressed and probed in response, but their much-changed team lacked incision and Southampton defender Maya Yoshida went closest to levelling the scores when he perilously flicked Mohamed Elneny’s free-kick just wide of his own goal.
The visitors had seen earlier counter-attacks fizzle out, but they sliced through the makeshift Gunners side to extend their lead before the break.
The Gunners had the lion’s share of possession but never looked competitive against Southampton, who named their strongest squad for the match.
The Saints’ seniors’ superior fitness and experience showed with Arsenal never looking like getting back in the game.
When Ryan Bertrand struck in the 38th minute, the game was over as a contest.
The left-back arrived in the box at the perfect time and beat his man to beautifully slot into the bottom corner.
In Aaron Ramsey, Alex Iwobi and Mohamed Elneny, the Gunners had Premier League regulars in their starting line-up – but without Alexis Sanchez, Theo Walcott, Olivier Giroud and Mesut Ozil, they lacked guile and bite.
Southampton had only won once in their last 23 visits to Arsenal, losing and in drawing last 20 matches.
After eliminating Arsenal, S’otons will play Liverpool in the two-legged semi-finals, with the first leg at St Mary’s in the week commencing 9 January.