A couple of weeks ago, Arsène Wenger admitted Alexis Sánchez looked “jaded”, the relentless Chilean’s workload taking a toll on even his machine of a body. Now, after a couple of weeks rest, Sánchez was back to his fizzing best, the driving force behind Arsenal’s 4-0 win against Swansea City, a bundle of energy that few defences can cope with, let alone the worst in the Premier League.

Sánchez seems to regard being substituted in much the same way as a giddy child playing in the park would after being unwillingly called home for dinner. When his number was put up, the game won and Wenger aiming to prevent him from similar fatigue in the future, he trudged towards the touchline as if he knew it was boiled cabbage waiting on the kitchen table.

Wenger did not seem particularly concerned at the very low-level show of dissent by Sánchez (“For me it’s a non‑story,” he said), and when he has a player of Sánchez’s ability it is not surprising he would tolerate the odd minor act of insolence. “Individually, you want everybody to behave well, but we don’t live in a perfect world,” Wenger said of a player whose enthusiasm to play every second of every game often has to be reined in. “He’s a guy who wants to fight everywhere, sometimes where he shouldn’t.”

After a week in which Dimitri Payet and Diego Costa proved not quite so enthusiastic about playing for their clubs, Sánchez’s desire to do the opposite might even be of some comfort to Wenger. “I have enough problems – I don’t need a Costa problem on top of that,” the Frenchman joked.

Sánchez scored one – a volley on the turn – and created another as Arsenal recovered from a creaky first half in which a more incisive side than Swansea might have done more with their early dominance. Olivier Giroud’s snaffled finish, after Sánchez’s cross fell loose in the area, made the home side’s initial advantage moot.

Arsenal will need Sánchez to be on top form, too. The win against Swansea took them to 44 points, enough to sneak them into the top four: at the same stage last season, that total would have put them top by two points. It is a state of competitiveness with which Wenger is unfamiliar. “It’s the first time in 20 years that at this stage of the season you have six teams at the top,” he said. “Chelsea still have a big advantage, but they’re all doing well. You look around you and nobody is dropping off, so it’s down to being consistent, keeping your nerve, focusing on your game. Now we go into Europe, into the cups, big games – who can maintain it? Honestly, nobody can tell.”

With such high levels and fine margins, a run of three winless away games starts to look like a minor crisis. Their defeats at Everton then Manchester City, followed by the last‑gasp draw at Bournemouth, represented their worst run of form on the road since the spell that essentially ended their title challenge in 2013‑14. Even then, it would not normally be especially calamitous, but when the competition is this fierce, a victory at Swansea became mandatory. “Our away form was brilliant at the start of the season – or most of the time,” said the goalkeeper Petr Cech, broadly an interested spectator for this game. “We had a loss at Everton and suddenly we had another two games where we dropped points. But today we gave the right answer, that it doesn’t matter and you have to carry on.”

This result, combined with Hull City’s victory against Bournemouth, sent Swansea to the bottom of the table again. The new manager, Paul Clement, stalked up and down the touchline in the manner of a man who knows, even with 17 games remaining, that time is rapidly slipping away, and that his side need to more than double their current points total of 15, in four fewer games than they have already played, to avoid relegation. In the Premier League’s 21 previous 38-game seasons, only three teams – Wigan in 2011‑12, Fulham in 2007‑08 and West Bromwich Albion in 2004‑05 – have survived from Swansea’s current position.

Perhaps Clement had Swansea’s next few fixtures in mind: before the end of February they have trips to Liverpool, Chelsea and Manchester City to cope with. “It’s not an eye-opener,” Clement said, as if trying to reassure everyone – possibly even himself – that he knew what he was doing when he accepted this job.

Clement is in something of a no-lose situation: should they go down it will be less his fault, more a series of poor decisions and institutional mistakes, but if they survive he will be carried around town shoulder high. He will have to produce something pretty special to earn that treatment, though.