Frantic, ragged, lucky, even at times rather desperate: oh yes, this was a hugely encouraging afternoon all round for Arsenal. If Arsène Wenger could have designed the perfect riposte to those familiar accusations of stylish underachievement – voiced last week by José Mourinho, a man who blurts out toxic barbs in much the same way some people feel compelled to make chit-chat about the weather – it would have been this, a raggedly full-blooded FA Cup victory against a Liverpool team who played the better football, created more chances, but still somehow always seemed likely to lose.

On a crisp, clear north London afternoon Arsenal looked like a team roused into a state of unaccustomed spikiness by the week-long hangover from that invertebrate 5-1 thrashing at Anfield. Abrasive for an hour, they were eventually hauled in as Liverpool's excellent three-man midfield began to dominate possession, but hung on not just to win but – even better – to win ugly, holding on to a 2-1 lead as Liverpool finished the stronger.

This was, above all, an excellent match, a reminder of the astringent qualities of a concussive February FA Cup tie, and an occasion from which both managers will take some encouragement. For an Arsenal team that had seemed to be drifting into battle-weary diffidence at exactly the wrong moment, there was a bracing sense of physicality about this performance, and above all a fine and decisive turn from Alex Oxlade-Chamberlain, the best player on the pitch for the opening hour.

It has been a timely return to full fitness for Oxlade-Chamberlain, who is still only 20 and has provided recently that vital sense of textural variation in an Arsenal team which, without Theo Walcott and Aaron Ramsey, can seem intent on trying to persuade the opposition to death.

Not here though, as at times there was almost a sniff of a pre-modern Arsenal about this Cup team of convenience as Mathieu Flamini, a leaping, drop-kicking Cato to Steven Gerrard's inspector Clouseau, hurled himself into tackles, half-tackles and never-were-tackles, and Oxlade-Chamberlain gave Aly Cissokho a traumatic opening hour playing as an orthodox right-winger. Here Arsenal's No33 was a blur of speed and intelligent short-passing, scoring the first and setting up the second, always playing with his head up, and looking the model of a fluid creative attacking midfielder.

There was a hugely encouraging sense of composure about his assist for the decisive second goal just after half-time as he took the time to look up and place a perfectly measured pass into Lukas Podolski's path for a first-time finish low beyond Brad Jones. Raheem Sterling also had an excellent match on Liverpool's left flank, showing excellent touch and control under pressure. Roy Hodgson has spoken about his willingness to create an England team full of pace and youthful vim. It will mean little if he ducks the chance to take the two best wide players on the pitch here with him to Brazil.

If Oxlade-Chamberlain was the brain behind Arsenal's victory, Yaya Sanogo was the galloping brawn. A 21-year-old with 11 career goals and just 39 Arsenal first-team minutes to his name, Sanogo started here in place of Olivier Giroud, who was finally given a rest at the exact moment he might have been better off getting out of the house for a bit.

Sanogo is an encouragingly mobile 6ft 3in centre forward, albeit there is still a gaucheness to his touch and a puppyish quality to his unceasing movement across the front line. He was brilliantly willing here, bullocking about like a young John Fashanu, and playing his part in Arsenal's opening goal by tussling repeatedly with Martin Skrtel, then chesting down the ball and shooting as Skrtel came charging out in search of Mesut Özil's corner kick. From the rebound Oxlade-Chamberlain tucked the ball home neatly.

After which Sanogo sprinted and wrestled gamely, one piece of closing down on Skrtel drawing a furious leaping ovation. And with half-time looming there was further evidence of something odd in the air as Mesut Özil won the ball with a fierce challenge on the halfway line – while across north London the dogs miaowed and the clock struck 13 – to set Oxlade-Chamberlain off again down the right. As he was at Anfield, Özil was energetically double-hustled by Liverpool's midfield. His problem right now is not so much that teams have learnt to do this to him, but that he shows such an obvious displeasure in finding himself harried and chivvied. This, it would seem, wasn't in the brochure. His quality remains, though: the pass down the right flank to put Oxlade-Chamberlain in space for the second goal was superbly finessed.

For Liverpool this was a frustrating afternoon. They were the better team on balance, particularly in the second half, with Luis Suárez producing another dashed off masterpiece in ferrety and instinctive centre-forward play and Sterling and Daniel Sturridge both incisive on the ball. Gerrard deservedly pulled one back with a penalty and they should have had another as Suárez was barrelled over by Oxlade-Chamberlain.

This, though, was destined to be the Ox's afternoon, reward for a performance of both maturity and youthful zest. However breathlessly Arsenal are still in the running in three competitions, although realistically the Cup is their best chance of an actual, non-metaphorical trophy this season. Ragged, flukey, hot-blooded, hanging on for dear life: who knows, maybe it might just be their year after all.