There was some late anxiety to endure as Crystal Palace, sensing another late rally might be rewarded, flung themselves into desperate pursuit of an unlikely equaliser, but Arsenal are back to counting this corner of south London as a home from home. They had retreated battered and bruised by a chastening defeat at this venue in April, yet they had not benefited from a fit Jack Wilshere in their ranks on that occasion. Times have changed.

The England midfielder was at the heart of everything impressive they tried here, spiky in the tackle and mature with his positioning, and a creator of his team’s decisive third goal with a carefully lofted pass over Palace’s back-line for Alexis Sánchez to collect on his thigh and poke into the corner on the gallop. The Chilean’s form, perhaps predictably, is flickering back into life with the transfer window so close and his contract ticking down. Wilshere’s deal, too, expires in the summer, though arguably the visiting fans’ best news of an encouraging night was the midfielder’s post-match assertion that he was sure a new contract “will get done”.

On this evidence, he is rightly restored as the side’s fulcrum, his metronomic presence a source of reassurance for a team who have been prone to panic at times. “Jack is coming back in competitive shape and gives something to the team at the moment,” said Wenger. “People who don’t have long contracts are questioned, always. But as long as you are somewhere, you give your best. The best way to show they are committed is to give that kind of performance. I felt Sánchez was very good from the first minute. This kind of Sánchez is a great football player, as we know. That’s the kind of performance we want from him.”

Possibly more disconcerting was the sight of the forward looking nonplussed – perhaps more bemused than infuriated – to discover only a handful of team-mates had joined him in front of the away support to celebrate Arsenal’s second goal. Sánchez, all short back-lift and frightening power, had ripped his shot through James Tomkins’ legs and inside Julián Speroni’s near post, but plenty of his colleagues preferred to celebrate together nearer the halfway line. It had Thierry Henry chuntering up in the Sky studio, though, in truth, it is easy to read too much into apparent splits when, in reality, raw emotion at a lead restored had probably taken over. The problem is observers will continue to scrutinise the body language until Sánchez’s time at the club is either extended or ends in divorce.

The thought of losing a player of his calibre feels all the more troubling in the aftermath of a performance this scintillating, even if all of Arsenal’s attackers had purred through the opening period. Comfortable with a back three and far more sprightly than tentative opponents, with Palace so nervous as runners infiltrated their lines, the visitors should have ended the contest by the interval. Nothing illustrated their superiority better than Sánchez’s delicious diagonal slide-rule pass beyond Tomkins for the on-rushing Mesut Özil to flick goalwards, only for Speroni to thrust out a left hand instinctively and paw the attempt away. The German would waltz through the centre again before the half was out, this time undoing his work with a heavy touch, but by then Arsenal were ahead.

After Palace failed to clear their lines Alexandre Lacazette was permitted to turn inside and curl a left-footed shot which was only pushed out by the diving Speroni. Shkodran Mustafi, alone beyond Martin Kelly at the far post, calmly side-footed into the net. Sánchez, standing with one foot beyond the back-line, had made a vague attempt to reach Lacazette’s effort, but the offside appeals were half-hearted. So had been much of the hosts’ play with frustration eventually overcoming Wilfried Zaha who was booked for dissent as the teams departed for the interval. At least he spent half-time channelling that exasperation into a positive response. He, and Palace, were unrecognisable as an attacking force thereafter.

Andros Townsend, after Zaha’s dart beyond Calum Chambers and pull-back from the byline, side-footed the hosts level and they might have led had Chambers not blocked Ruben Loftus-Cheek’s attempt. Even Arsenal’s flurry of goals around the hour-mark did not knock the stuffing from the home side’s approach and Zaha, mistiming a header in front of goal, and Bakary Sako might have scored before Tomkins nodded home as full time approached. That was Palace’s first goal from a set piece this season – so much for such routines being their forte – and provoked late anxiety, but Wenger’s side maintained their composure to survive.

This defeat ended Palace’s eight-match unbeaten run and left them a point above the relegation zone. To make matters considerably worse, Manchester City are their opponents at Selhurst Park on Sunday to confront a patched up side. Yet, while Hodgson juggles his options, Arsenal are buoyed. Sunday’s trip to the Hawthorns, another venue where they had sunk without trace last season, suddenly feels like an opportunity.