The Southampton players, Virgil van Dijk such a towering presence in their number, were saluting a giddy travelling support long after the final whistle here. This club has waited three decades to force passage into a League Cup semi-final, but the new year will bring a collision against those same opponents from 1987, Liverpool, and thoughts of Wembley. They will be thrilled at the prospect of further progress.

This squad will not be daunted by the prospect of confronting Jürgen Klopp’s side, whose 6-1 win at St Mary’s had jettisoned Southampton from the fifth round last year. Claude Puel, with only three starters retained from the weekend, could point to this victory as evidence of strength in depth as well as real cause for optimism. Few visiting teams will prevail as comfortably as this at the Emirates, hassling and harrying opponents who had not been beaten since the opening weekend, and ensuring their advantage was established early. Theirs was the swagger, the experience and all the bite on show.

It said everything that, when Arsenal would normally have expected to be laying siege to their opponents’ goal late on, it was their goalkeeper, Emiliano Martínez, blocking sharply from Pierre-Emile Hojbjerg’s shot, and Ainsley Maitland-Niles hacking Sam McQueen’s attempt from the goalline. Arsène Wenger bemoaned a lack of urgency in the first half which allowed Southampton to build their lead, but neither did his side whip up a frenzy of late opportunities when they were chasing the game. “Disappointing” was his verdict of the whole occasion, with the home support making clear their disgust at half-time and full-time. One route to silverware has been blocked off. It was as if the 19-match unbeaten run counted for little.

Southampton merited everything they achieved. Their authority was personified by Sofiane Boufal’s display, the Moroccan revelling in only his third start for the club since a record £21m arrival from Lille in the summer. He tormented back-tracking Arsenal players whenever the visitors countered, gliding away from his markers with menace. It was his first-time shot from Ryan Bertrand’s cutback 13 minutes in which Rob Holding blocked, only for the ball to run free to Jordy Clasie just inside the area. The Dutch international instinctively belted the loose ball into the corner with glee to register a first goal for the club.

The reward had been sparked by Maya Yoshida’s glorious crossfield pass from deep for Bertrand to collect but, in the relative simplicity of its construction, the goal exposed Arsenal’s fragility across an unfamiliar back line. The home side’s huff and puff in the period after the goal never threatened to force an equaliser. Then Harrison Reed snapped at Aaron Ramsey to steal back possession and, via a touch from Bertrand, the busily impressive Steven Davis supplied Boufal down the left.

The forward teased space from Gabriel before liberating Bertrand on the edge of the box and, with one touch to gather and another to spit his shot away before Holding could suffocate the attempt, Southampton’s lead was doubled. Martínez, perhaps unsighted by the clutter of bodies ahead of him, reacted late and the ball scuttled unchecked into the corner of the net.

“We were clinical in that half, two chances and two goals, and I like this,” muttered Puel through a smile. “We actually created many more chances in the second half and could have made the game safe, but it was still a fantastic result for us. Good solidarity, good attitude. I enjoyed what my players did.”

Boufal and McQueen might have added the third well before Wenger flung on Alex Oxlade-Chamberlain in desperate pursuit of the tie. The best Arsenal managed all night was arguably the England international’s dreadful attempt from Granit Xhaka’s clever touch, the ball arcing horribly over the bar. But Fraser Forster would not be beaten, with Yoshida and Van Dijk so resolute ahead of him.

This Southampton team boasts rare quality, particularly when one considers Charlie Austin, Nathan Redmond, José Fonte and Cédric Soares will be back for the Premier League game at Crystal Palace on Saturday. Their mid-table position in the top flight seems like a deception on nights such as this, and is perhaps primarily a reflection of having to juggle domestic duties with an attempt to progress in the Europa League. But this competition is offering the most immediate prospect of silverware.

“Arsène just told me to go on and win it,” said Puel when asked about his embrace with Wenger, once his manager at AS Monaco, at the end. By then the away support were in full voice while the locals grumbled towards the exits.