Wayne Rooney has not made a habit of enjoying his professional meetings with Mesut Özil. The horrors of Bloemfontein at the last World Cup may never be expunged fully, while being left on the bench as Manchester United were eliminated from the Champions League by Real Madrid clearly stung. This, though, was an afternoon of counterattack for English football's own distinct workaholic take on the modern No10 role – and a chastening experience for Özil, who was Arsenal's most disappointing player on what was at times a brutally physical afternoon of distinctly British football. Welcome to Wayne's world.

In the buildup, Özil had announced that Arsenal would be travelling to Old Trafford to "have fun". Özil can say things like this, a player of wide and winning experience who earlier this year ran himself to a sweat-soaked standstill on this ground as Real Madrid won that excruciatingly tight Champions League quarter-final. Özil didn't have much fun here though. It always seemed likely these contrasting leaders from between the lines, Özil the pickpocket who comes to life only in spurts, Rooney relentless in his attempts to batter down the door with guile. And while it will be tempting for some to read too much into this result – this was not the same old Arsenal and they will be far from devastated by a narrow 1-0 defeat – when it came to the match within a match there was only one winner.

From the start Rooney seemed most energised by the challenge of a boisterously alive Old Trafford. It is fashionable to roll the eyes slightly at the Premier League's much-trumpeted straining muscles, but the fact is the challenge is a little different (this is a league where you can still "win" a shoulder barge, as Rooney did twice in the second half). And while Özil is allowed to have a poor game, it is hard to block out the memory of those unkind whispers on his departure from Madrid about his conditioning and stamina. There was a telling moment with 15 minutes left here when Rooney was booked for a full-length late tackle.

Necks were craned briefly to see if it was perhaps his opposite number writhing on the ground. But no. Özil was safely wandering off up the right wing 40 yards away. Work rate, hunger, desire: these things are some way off being everything in football. But they are definitely something.

It is no secret that Rooney loves playing against Arsenal, going back 11 years to the goal that launched a thousand white-Pelé analogies, and he remains that rare thing, an English player openly admired by Arsène Wenger. He was wonderful here, offering the full range of his mixed bag of Rooney-isms: from the lovely attempted scoop pass at the start of the second half, evidence of a man operating with his blinkers off, to his relentless work rate, not just in spurts but in every passage of the game. By the end Rooney had run almost 11km, bettered only by Aaron Ramsey. He did it from centre-forward too, every one of those scampering bursts a work of attacking intent, or above and beyond defensive foraging.

Even the game's only goal was as close as a header from a corner is likely to get to being a moment of instinctive interplay. Rooney's kick was whipped toward the near post, Robin van Persie's run perfectly timed to take him into a kind of between-the-zones region, a Gaza of the Arsenal defensive plan. It looked like a planned move, both in its execution and the pointedly fraternal celebrations between United's two strikers.

For Özil there was only disappointment on the biggest occasion of his Arsenal career to date. He started just behind Olivier Giroud here in a direct match-up with Rooney, perhaps with a view to testing Nemanja Vidic with his speed and lateral mobility. In the event he was largely anonymous in the first half, so much so that as he dropped deeper behind Ramsey it had the air of a withdrawal, of a man taking breath to find some space in the game.

He did better in the second half after moving to the right, having Arsenal's first actual shot at goal after an hour's play, and for a period there were glimpses of the best of Arsenal's record signing, the subtle movement, the constant peripheral awareness Rooney perhaps at times runs around too much. But what a player you would have if you could blend only their respective strengths, taking a pinch of Rooney and wrapping it up in Özil's.

Arsenal, it must be said were far from disgraced, outplayed, or overrun. These Super Sunday-ish collisions are so often presented in a farrago of swirling overstatement – seasons defined, destiny shaped, lives ruined, civilisations decimated – but Wenger will take encouragement from this performance. He is, though, entitled to expect a little more from his chief conductor.

At the end Özil turned and walked straight to the tunnel without even a wave to Arsenal's fans. He is too good not to learn back from the experience – and for once, perhaps, from his opposite number here.