The Gunners had two early chances via Max Dowman and Gabriel Martinelli, with the latter's effort superbly blocked by Taylor Harwood-Bellis. But Southampton were not overawed. Loo Scienza raced through one-on-one with Kepa Arrizabalaga before being successfully marshalled away from goal by Cristhian Mosquera.
Southampton stopper Daniel Peretz was called into action to parry away Martin Odegaard's strike. He had another chance moments later, blazing a close-range effort over the bar, much to Arteta's frustration. And he would have felt much worse when Ross Stewart fired the Saints ahead with a clinical finish at the end of a swift counterattack, as James Bree's ball looped over Ben White and allowed the Scotsman to fire home past Kepa on the 35-minute mark.
Dowman had a chance to net an equaliser when his effort was blocked by Ryan Manning, but it was Arsenal's uncharacteristically sloppy play at the back that was almost their undoing once again. Gabriel gifted the ball to Tom Fellows with a lackadaisical cross-field pass, but blasted his shot over the target. Scienza then came agonisingly close to scoring a second Southampton goal in stunning fashion, cutting inside from the left before unleashing a right-footed strike which cannoned off the bar.
Arsenal's Iktor Gyokeres made the desired impact when he slotted home from Kai Havertz's cut-back after the German was found by Gabriel's through ball. Arsenal would have been tipped to go on and win the tie from that point, and Dowman had his sights on being the match-winner with a fine left-footed strike that was tipped behind by Peretz.
Martinelli then shot wide from the resulting corner, but amazingly, it was Southampton who struck next. Fellows made a driving run forward and laid the ball into the path of substitute Shea Charles, who calmly placed a fine finish past Kepa, which went in off the post in the 85th minute.
After six nerve-shredding minutes of stoppage time for the hosts, Tonda Eckert's men held on for a famous victory and a place in the semi-finals.
Speaking to the press after the match, a frustrated Artera took full responsibility for the shock loss.
"I love my players, what they have done for nine months," he reflected.
"I'm not going to criticise them for losing here. What they are putting their bodies through, some didn't have to be here today. I'll defend them more than ever.
"If someone has to take responsibility that's me. We have the most beautiful period ahead of us. Normally you have two or three moments like this in a season, this is the first moment with a level of difficulty. Let's stand up and make ourselves count.
"No excuses about players that are missing or that are here with issues. Let's look at ourselves in the mirror, accept the situation, rebel against it and go forward with clarity."