It was a game of great saves and awful defending, of fine attacking play and gripping twists in the narrative, and there was a redemptive ending for the enduring frustration that is Danny Welbeck. The drama was relentless and for neutrals there was the bonus of seeing the contest descend into chaos after Jack Wilshere’s clash with Jack Stephens in added time.

Yet Southampton departed with an empty feeling. They had teased their supporters with the rarity of a Shane Long goal and their pursuit of an equaliser during the second half had yielded a reward when Charlie Austin, who had entered the fray moments earlier, cancelled out Arsenal’s lead with his first touch in the 73rd minute.

A precious point was there to be snaffled and, having ruined their first league game under Mark Hughes with a wretched collapse against West Ham last Saturday, that unfamiliar sensation Southampton were experiencing was a surge of optimism.

Yet the speed with which it was replaced by despair encapsulates why their hold on their Premier League status remains so uncertain. They had been level for eight minutes when Dusan Tadic allowed Alex Iwobi to cross for Welbeck, who had just produced a contender for miss of the season, to rise above Cédric Soares and head home Arsenal’s winner. “At that point you need to have clarity of thought to make sure you take something out of the game,” Hughes said.

There are six games left for Southampton, who are three points below 17th-placed Crystal Palace, and Welbeck’s second goal was the cue for a loss of composure from Stephens, who accepted the bait when he felt Wilshere nibbling at him. Wilshere was in full wind-up-merchant mode as Southampton attacked and the frustration was too much for Stephens to bear.

It was a naive reaction and the way the centre-back lashed out left Andre Marriner with no option but to send him off. Mohamed Elneny would follow him down the tunnel – Arsène Wenger suggested Arsenal could appeal against the Egyptian midfielder’s dismissal for pushing Soares – but the damage was already done.

“Wilshere should have been sent off,” Hughes said. “Jack Stephens has reacted to being pulled back for about 20 yards. It’s not correct but it’s understandable. But if you’re going to send Jack off, you have to send Wilshere off for bouncing up. I thought I saw a definite movement with his knee towards Jack.”

Wilshere escaped with a booking and Hughes was left to reflect on Southampton’s failure to take advantage of opponents whose minds were elsewhere for long spells. The visitors began with a cautious 5-4-1 system, with the return of Oriol Romeu giving the midfield a steelier look and Long foraging on his own up front. Yet they had players who could trouble for Arsenal on the break and James Ward-Prowse had an early effort hacked off the line by Héctor Bellerín.

The opening stemmed from an error from Shkodran Mustafi, who was an accident waiting to happen in the heart of Arsenal’s defence, and Southampton’s reward arrived in the 17th minute. Sead Kolasinac allowed Soares to squeeze in a cross from the byline and Long nipped in front of the motionless Mustafi to prod his second goal in 46 appearances beyond the exasperated Petr Cech.

Wenger’s decision to rest seven players before his side’s trip to CSKA Moscow for the second leg of their Europa League quarter-final on Thursday demonstrated where Arsenal’s priorities lie. Their challenge for a place in the top four is all but over.

However, they equalised with their first coherent attack, Welbeck conjuring a beautiful flick from Iwobi’s pass, the ball running into the area for Pierre-Emerick Aubameyang to elude Stephens and beat Alex McCarthy. Aubameyang’s sixth goal since his arrival from Borussia Dortmund settled the mood and Southampton’s porous defence was again exposed when Welbeck scored in the 38th minute. Iwobi found him and the striker sped past Stephens before seeing his powerful shot hit Maya Yoshida, whose punishment for turning his back on the ball was to watch it fly into the right corner.

Southampton chased an equaliser, Long and Pierre-Emile Højbjerg testing Cech, Wesley Hoedt forcing Elneny to clear his header off the line. Long turned in Højbjerg’s wayward shot, only for the flag to go up for offside.

Wenger introduced Wilshere in place of Reiss Nelson, who faded on his first Premier League start but a goal from the visitors felt inevitable. Soares drove inside from the right and Austin, who had just replaced Yoshida, converted his cross.

Cech denied Austin a second a few minutes later and Southampton must have thought their luck was in when Welbeck turned Wilshere’s cushioned ball over an unguarded net. They were wrong.