Panic over. After a frustrating start to the season Arsenal have finally flourished, outclassing Watford in a first half they illuminated with excellent approach play and clinical finishing. The only significant criticism would be the failure to sustain their superiority for the full 90 minutes, allowing a home side that had been humbled before half-time to find a measure of encouragement in the latter stagesbut though the Hornets wrestled their way back into the contest they never looked likely to avoid losing it.

On Friday Wenger had been asked whether his recent transfer dealings – for Shkodran Mustafi and Lucas Pérez – were motivated by desperation. “Look at my face,” he responded. “Is this the face of someone who tends to panic?”

A day later he might have enjoyed the expressions on a few Watford defenders as his side displayed the kind of creativity and ruthlessness that would have even their manager’s harshest critics purring.

Mesut Özil, who made his first start of the season, was at the heart of much of their finest football, with Alexis Sánchez also outstanding, winning a penalty, claiming an assist and scoring a goal of his own against an unfamiliar, and unconvincing, Watford back three.

The patched-up nature of Arsenal’s defence had been a feature of the early season but this time it was their opponents’ rearguard that was significantly weakened. With Craig Cathcart injured and Miguel Britos given leave to attend the birth of his child, there were league debuts for Younès Kaboul and Christian Kabasele, who played either side of the mountainous Austrian Sebastian Prödl. “Today, at the last minute, we lost two starters,” said Walter Mazzarri. “In a squad that is being built and is growing game by game it is difficult to cope, and there were some mistakes.”

Arsenal swiftly worked out a way through the restructured backline, with the first hint of the trouble ahead coming in the sixth minute when Sánchez’s chipped pass found Özil bursting into the area but offside. Two minutes later the pair repeated the trick in reverse, Özil this time lofting the ball into the box, but before the Chilean could bring it under control he was caught by Nordin Amrabat’s elbow. Kevin Friend took so long to give the penalty Watford had assumed there would not be one, and on the touchline Mazzarri burst into furious gesticulations when the referee finally pointed to the spot. The Italian refused to directly address the award after the game but spoke about “two episodes that nobody in the stadium really understood”, presumably also referring to the bewildering decision to penalise Amrabat for taking the ball past Laurent Koscielny on the right wing in the 37th minute.

Undeterred, Santi Cazorla stroked his penalty down the middle to kickstart a difficult first half for the home side. However it took another 25 minutes before Özil and Sánchez combined again with any real menace, as a smart one-two on the edge of the penalty area led to a low shot from Sánchez that was saved by Heurelho Gomes.

In the intervening period Watford had occasionally threatened, with Amrabat particularly industrious on the right. It was from one of his crosses that Watford came closest to an equaliser though it was Koscielny who nearly scored it, his miscued clearance forcing Petr Cech into a smart save.

Having fought their way to an approximation of parity on the run of play, the last five minutes of the first half turned out to be very long ones for Watford. First they were sliced open by an excellent, swift counterattack which ended with Sánchez mis-hitting Theo Walcott’s fine cross goalwards, the ball bouncing just over the line before it was cleared. Then in the final moments of stoppage time Sánchez was given a preposterous amount of time and space on the left wing, and he was the only player on the pitch to spot Özil’s late sprint into the penalty area. His centre was precise, and appropriately despatched.

Alexis Sánchez’s mishit effort squeezes over the line to give Arsenal a two-goal cushion. Photograph: Andrew Boyers/Reuters

Mazzarri brought on Roberto Pereyra, the recent arrival from Juventus, at half-time – he said he did this “to try to surprise Arsenal” though having him spend half-time warming up on the pitch rather gave the game away – while Daryl Janmaat and the deposed record signing Isaac Success also made their debuts from the bench. Their arrivals, and a switch to a back four, galvanised the side and they scored when Janmaat’s cross was half-cleared to Étienne Capoue, whose blocked shot fell to Pereyra, who took a touch and found the corner from eight yards.

Thereafter Odion Ighalo twice came close to bringing if not panic then at least a flicker of concern to Wenger’s face, but with a lead to protect the Gunners were increasingly content to contain and occasionally break. Walcott and Alex Oxlade-Chamberlain both sent attempted chips over the bar; for Arsenal, everything is looking up.