The noisy neighbours have been put in their place for now. By the time Harry Kane and Dele Alli trudged off the pitch in the dying stages, with the triumphant taunts from the home fans ringing in their ears, Tottenham Hotspur had long let go of the notion of offering swaggering proof of where the balance of power in north London lies these days. Instead, it was an afternoon of pure release for Arsène Wenger, who took great joy from a first derby win over Mauricio Pochettino and a performance that reminded Arsenal of better times.

There could be no dispute about Arsenal’s ownership of the local bragging rights, earned thanks to goals from Shkodran Mustafi and Alexis Sánchez in the first half, not to mention a blend of defensive resilience and midfield resilience not always associated with this team of late. The only frustration for Wenger was that his players do not produce this much class and poise more consistently.

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Arsenal’s first victory over a fellow big six member this season was assured long before the final whistle and it took them to within a point of Tottenham, whose title hopes are fading after a strangely muted failure to rise to the occasion. For all that Pochettino preferred to focus on the officiating, from the award of the free-kick that led to Mustafi’s opener to the failure to spot that the German was marginally offside from Mesut Özil’s subsequent delivery, to Granit Xhaka escaping with a booking for a clumsy early foul on Alli, questions over his young team’s mentality will persist until they win this type of game. The disappointment was even more bitter than when they faltered at Old Trafford a month ago.

It was certainly unusual to be at this fixture and detect early foreboding in the home sections, where there was queasiness at the thought of Tottenham jabbing at the soft underbelly of late-era Wengerball. To appreciate the shifting dynamics in this corner of the capital, one only had to glance at the teams’ midweek assignments in Germany: while Arsenal, demoted to the Europa League, visit the Bundesliga stragglers Köln on Thursday, Tottenham can clinch top spot in their Champions League group at Borussia Dortmund two nights earlier.

Yet the idea that they could ever be underdogs against these opponents compelled Arsenal to tear up the narrative. The atmosphere was noisy and intimidating and the home side offered the impression that they had something to prove after an underwhelming start to the season. They pressed Tottenham urgently and Alexandre Lacazette had an early sighter after Eric Dier dithered in possession.

Lacazette, starting with Sánchez and Mesut Özil for the third time in the league, was a sprightly opponent for the Tottenham defence. The striker hurried Hugo Lloris into a panicked clearance, almost converted Héctor Bellerín’s low centre after a fine pass from the impressive Aaron Ramsey and sparked jubilant scenes when he set up Sánchez for Arsenal’s second goal.

It was an uneven offering from Tottenham. Toby Alderweireld was missed in defence, Kane wore strapping on his right leg, Alli did not look fully fit after missing England duty and Harry Winks was ready only for a place on the bench, meaning that the visitors lacked control in midfield. Moussa Sissoko was careless in possession and Mousa Dembélé struggled with Arsenal’s tempo.

Tottenham did have their moments before Mustafi’s controversial opener. There was danger whenever Christian Eriksen found pockets of space behind Ramsey and Xhaka and Kane operated a shoot-on-sight policy.

However, Petr Cech foiled Kane on two occasions, most notably when the striker broke down the left following miscommunication between Laurent Koscielny and Mustafi while Arsenal’s back three contained Alli. Eriksen clipped Cech’s right post with a low shot, but Arsenal’s football was silkier.

The game turned on a couple of tight decisions. First, Mike Dean penalised Davinson Sánchez when the Colombian tried to tackle his namesake in red and white. Özil floated the free-kick to the far post from the left, the flag stayed down and Mustafi escaped Jan Vertonghen to send a looping header beyond Lloris, the ball going in off the inside of the right post almost in slow motion.

Tottenham’s response was torpor, enabling Arsenal to tear into them. Lacazette’s elusive movement took him beyond Tottenham’s high line after a clever pass from Bellerín and his ball found Sánchez, who crashed a high shot past Lloris despite a heavy first touch.

Facebook Twitter Pinterest Alexis Sánchez smashes home Arsenal’s second. Photograph: David Klein/Reuters

Jesús Pérez, Pochettino’s No2, remonstrated with Dean at the interval, but the main worry for Tottenham was how Arsenal’s greater energy in midfield allowed the attacking triumvirate of Lacazette, Özil and Sánchez to flourish. Sánchez had his most productive game of the season and Özil earned a standing ovation. Wenger praised his two contract rebels.

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Arsenal could not entirely relax with a 2-0 lead. Tottenham sought a riposte and Mustafi had to make a superb block when Eriksen released Kane, while Cech made a late save from Dier’s header.

Yet Arsenal held out with surprising comfort. Pochettino introduced Fernando Llorente and Son Heung-min, but Tottenham never looked capable of mounting a heroic comeback. Arsenal relished silencing talk of a power shift.