Santi Cazorla offers a two-footed, subtly skilful rebuke to those critics who claim Arsène Wenger has lost his touch in the transfer market . Equally importantly, a creator described as a cross between Liam Brady and Cesc Fábregas appears sufficiently talented to serve as an on-field airbrush, smoothing out the imperfections in other areas of Arsenal's class of 2012-13.

Admittedly the impressive Abou Diaby enjoyed a key ball-winning role for the visitors but Wenger's £12m acquisition from Malága created Arsenal's first goal before scoring the second himself. It was Cazorla, deployed in a central role behind Olivier Giroud in a 4-2-3-1 formation, whose smart link play enabled his new side to dominate possession and control the tempo for prolonged periods.

Far too brainy to be cowed by Liverpool's embryonic pressing game, he ensured that what the home manager, Brendan Rodgers, terms as the "transition" – the phase of play when his side are striving to reclaim the ball – was frequently considerably longer than intended.

Like Rodgers, Wenger is a "conviction coach" who, refusing to have truck with the pragmatic tactics and "consensus" politics of many managerial peers, sticks to his slick passing, sensible spending principles come rain or shine.

As the trophy-less years have accumulated, Arsenal's manager has sometimes seemed a bit of a prophet in the wilderness but, much more of this, and his cynics may start revising some gloomy pre-season predictions.

Certainly watching the impressive Lukas Podolski – all intelligent, diligent, running in a wide-left role – meet Cazorla's clever pass before scoring his side's first goal of this Premier League campaign, Wenger must have suddenly felt reassuringly warmed by Anfield's weak afternoon sunshine.

The pain inflicted by the loss of Fábregas and, more recently, Robin van Persie – not to mention Nuri Sahin's decision to join Liverpool on loan from Real Madrid – was temporarily at least diminished by his new 5ft 6in Spaniard.

"We saw very quickly that Cazorla was not going to take six months to settle," Wenger said. "And we know Podolski is deadly when he gets a chance." Blessed with what coaches call "soft feet" – because they cushion and caress the ball so well – and sharp vision, the former is the sort of player fans struggle to take their eyes off.

From Giroud's viewpoint this could only be a good thing. Long before Cazorla had assuaged Wenger's anxieties – not to mention ruined José Reina's afternoon – by scoring Arsenal's second goal, their lone striker had appeared a weak link.

It is all very well boasting a remodelled defence which has gone three games without conceding, but memories of Van Persie will keep rearing their head if the ball persists in bouncing off Giroud like this. Forget the glorious first-half chance missed by the French forward, if only his hold up play had been a bit better much good work from Cazorla, Diaby and Mikel Arteta would have reaped even greater dividends.

These are, of course, early days and expectations are, as Wenger puts it, very high. Giroud must be given a decent chance to adapt to a new football culture but it is impossible to resist the thought that a move for Andy Carroll on Arsenal's part last week might not have been quite as left-field as it sounds. Alan Pardew, Newcastle United's manager, sees shades of Zlatan Ibrahimovic in the England centre-forward and what better habitat in which to coax them out of him than The Emirates?

While Liverpool loaned Carroll to West Ham, Arsenal twice attempted to sign Yohan Cabaye from Newcastle before the transfer window's closure but Wenger surely did not need the France playmaker. Indeed, with Jack Wilshere scheduled to make his long awaited return from ankle and knee injuries next month, midfield looks the Gunners' strong suit. Here it was sufficiently rich for Aaron Ramsey and Theo Walcott to be named as substitutes while Alex Oxlade-Chamberlain's frequent struggles to get beyond José Enrique barely mattered.

"There's quality and a fight for places in our midfield," said Wenger, "and Wilshere's looking very good in training."

Carl Jenkinson's encouraging emergence at right-back – even if Raheem Sterling did give him a couple of frights – has helped ensure that a defence protected by Vito Mannone, Arsenal's third-choice goalkeeper, also appears a more robust department than expected.

"It's encouraging," Wenger said. "It's early and football often offers lessons in humility but I'm confident we have good potential."

Maybe, just maybe, the manager who forecast the Eurozone crisis before many politicians and economists is finally poised to remind everyone that football clubs can occasionally win trophies and make money.