Arsène Wenger had better hope that Pierre-Emerick Aubameyang is a man of his word because this was the sort of listless performance that could easily prompt a rethink. Arsenal, as has been the case so often this season away from home, delivered a meek and spineless display that suggested it will take much more than a club-record signing up front to address their problems.

Just about everything that could go wrong did go wrong for Arsenal on a sobering night for their manager and players. They conceded within 60 seconds of taking the lead, Petr Cech then presented Swansea with their second goal when his awful miscue landed at the feet of the indefatigable Jordan Ayew and Arsenal’s ignominy was complete when Sam Clucas scored his second of the evening in the closing minutes.

Swansea, bottom of the league at the start of the day, deserve huge credit for ruthlessly exposing Arsenal’s weaknesses. They are now out of the relegation zone for the first time since the beginning of November and the turnaround since Carlos Carvalhal took over as manager from Paul Clement is truly remarkable. The sight of Clucas, who was a maligned figure six weeks ago, leaving the pitch to a standing ovation from the home supporters when he was withdrawn late on feels emblematic of just how much life has changed in these parts following the arrival of their Portuguese manager.

Swansea have picked up 10 points from five games under Carvalhal, won back-to-back league matches for the first time this season – against Liverpool and Arsenal – and look totally unrecognisable from the team that were sleepwalking towards the Championship barely a month ago. That Carvalhal has not added a single player to his squad in that time makes the transformation all the more impressive.

“We are very happy,” the Swansea manager said. “To win against Arsenal after beating Liverpool means I’m proud of my players. They deserve all the credit. I told the players we are ready to do something different and I said after the win at Watford we are not dead, we are breathing. We have a chance of staying up. We are not in intensive care but we are not far away from the doctor saying we can go home.”

Arsenal, as things stand, are far more in need of emergency treatment. Wenger was left bemoaning “huge and massive mistakes” as Arsenal played into the hands of a Swansea side that were set up to sit deep, frustrate and strike on the counterattack. That was Carvalhal’s game-plan and Swansea executed it perfectly in the second half in particular. The opening 45 minutes was a different story as Swansea accepted Arsenal’s invitation to attack them and created a succession of early chances.

It was half an hour before Arsenal fashioned an opportunity of note, when Alex Iwobi broke free on the edge of the area to drill a left-foot shot that Lukasz Fabianski turned behind. That rare attack proved to be a warning because three minutes later Wenger’s side took the lead. Mesut Özil was the architect, the German given far too much time and space to look up and deliver a perfectly weighted inswinging cross from the right that picked out the run of Nacho Monreal, who ghosted in behind Kyle Naughton to score.

Swansea’s response was instant and from Arsenal’s point of view it was a desperately poor goal to concede. Özil was guilty of losing possession too easily to Martin Olsson deep inside his own half and questions will also be asked about Granit Xhaka’s failure to track Clucas’s run as the midfielder burst on to Alfie Mawson’s threaded pass. Clucas made the next bit look remarkably easy as he took a touch to take the ball away from Laurent Koscielny before steering a fine left-foot shot inside Cech’s near post.

Although that equaliser was the least Swansea deserved on the balance of play in the first half, Arsenal dominated the opening 15 minutes after the interval. Chances, however, were few and far between as the home side defended resolutely and made it hard for Arsenal to play through them, prompting Wenger to introduce Henrikh Mkhitaryan.

Arsène Wenger instructs Henrikh Mkhitaryan as he prepares to come on as a substitute for his first Arsenal appearance. Photograph: Matthew Ashton - AMA/Getty Images

Within a minute, however, Arsenal conceded a second in farcical circumstances. Monreal elected not to keep the ball in play, much to Wenger’s anger, and Shkodran Mustafi, under pressure from Nathan Dyer, passed back to Cech from the throw-in that followed. On a sodden pitch the Arsenal goalkeeper sliced his intended clearance horribly and Ayew had the simple task of rolling the ball into the unguarded net from no more than eight yards for his seventh goal of the season.

In a final act of desperation Wenger introduced Olivier Giroud, who has all but agreed to join Chelsea, as Arsenal forlornly chased an equaliser.

Yet it was Swansea who struck again when Clucas, who caused no end of problems with his dynamic forward running, converted at the near post, leaving Wenger and his players to reflect on that all too familiar feeling away from home, where they have won three league games all season.