With 96 minutes gone in this agreeably fevered north London derby a small, stricken-looking man in a tracksuit could be seen leaping across the touchline at the Tottenham Hotspur Stadium, arms waving furiously, before being dragged back off the pitch by the fourth official.

Arsenal’s Nicolas Jover has been a pioneer of the fashion for set-piece coaches to pop up at every designated opportunity and assume a look of urgent command, apparently convinced that their presence sightly closer to the pitch, their personal voodoo, their revolving index fingers, will somehow affect events on it.

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On this occasion it seemed entirely justified. Frankly, as Guglielmo Vicario jogged forward into the Arsenal box and began literally wrestling with David Raya, a blur of slaps and grapples, vicious goalkeeper-on-goalkeeper action, you expected to look up and find Jover curled into a ball in the centre circle, iPad skimmed into the crowd, unable to compute this unplanned variation.

It was that kind of afternoon. Three goals up at the break, Arsenal invited their opponents back into this game, saw that invitation vigorously accepted, then managed to hang on at the end when all they really had left was hanging on. Spurs probably deserved a point. Arsenal probably deserved to win given the stakes.

In the end Arsenal won this game because for an hour they played with a commanding sense of control, led by a wonderfully fluent and incisive performance from Kai Havertz who scored one, made one and ran constantly in that upright, slightly insolent style.

It has been a common practice, most notably during his end times at Chelsea, to ask what Havertz actually does. What is he? What does he do? How do I process this thing? This is the Havertz shtick.

Well, here he played like Harry Kane. He dropped deep and passed beautifully. He held the ball with his back to goal. He won seven headers, made four clearances, tackled, intercepted, fouled, key-passed. He seemed at times to be operating in his own clean, clear space, romping about like a medical student on a fun run, but always deceptively quick and shark-like in his movements.

His best moment came in the move that made it 2-0 on 27 minutes. The goal was made by a dreamy, high-speed counterattack from left to right. There will perhaps be some outrage at the failure to award a Tottenham penalty for a couple of slips in the buildup. Far more damaging to their cause was the ease with which the Spurs midfield and defence were filleted in the seven seconds that followed.

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Bukayo Saka was part of the springboard, helping to ping the ball away in a lovely little triangle at the edge of the Arsenal penalty area. Saka set off on a straight sprint out into the open spaces on the Spurs left. Havertz saw what was happening, ran the numbers, saw the space and in that moment stopped, just enough, appreciating in the middle of all that noise that this was now about execution not speed. The pass was perfectly flighted into Saka’s stride. He cut inside, leaving Ben Davies sliding into next season, then curled a low hard shot into the far corner, a brilliant finish.

Arsenal were already 1-0 up by then. It had come from a corner, whipped in by Saka, skimmed into his own net by Pierre-Emile Højbjerg, and met with a sudden silence around the ground, the own goal double-take, broken by a delayed explosion from the far away end, then joined by another angry wave of noise as Saka repurposed some goading from the Spurs fans into a provocative ear-cup celebration.

Havertz got the third shortly afterwards, from yet another Jover-drilled set piece. Once again he seemed to be operating in his own time zone, hovering unmarked then bulleting a fine delivery from Declan Rice into the net.

The goal made it eight plus five assists for Havertz in 15 games since mid-February, coming on strong at the sharp end of the season. What kind of player is he? Who knows, really. A slightly fey Germanic Drogba perhaps? He certainly likes the big games. He likes the physical challenge, too.

Havertz has won 85 headers this season, 12th on the list in Europe’s top-five leagues for attackers and midfielders, more headers than Niclas Füllkrug and Wout Weghorst. He makes and scores goals. He has that nice little edge of spikiness. Arsenal probably do need to sign a killer. But they already have a fine stealth centre-forward.

Otherwise this was an excellent game on a lovely day for football, chilly and clear and just rainy enough. Spurs had a goal chalked off for a micro-offside. They hit the post. They were invited back in by a horrible mistake from Raya, but also by their own energy levels as Arsenal tightened up a little but still had enough to take it at the death.