We’re coming for you, we’re coming for you. Oh Tottenham Hotspur, we’re coming for you. At the end of a raucous, fun, potentially vital Premier League afternoon at the Emirates the home fans had already turned their eyes towards the other power in north London.

Last month, as Tottenham buzzed about just behind the top two, it became fashionable to point out that winning the league was “in Tottenham’s own hands”. Which is, of course, the least secure place of all to be for winning the league. A 2-0 victory here, the first Premier League defeat of Ole Gunnar Solskjær’s time at Manchester United, means Arsenal have now made up nine points on Spurs since Valentine’s Day and lurk a single point behind in fourth.

Unai Emery will be less concerned with the balance of north London enmity. This was a hugely significant result for the trajectory of Arsenal’s new managerial era, a springboard for the slog through spring that offers the most obvious measure of success in Emery’s first season. There were two reasonable goals back in August. First, to make everyone feel better and create a sense of purpose again at the heart of this listing red and white corporate machine. Secondly, and more tangibly, to get back in the Champions League, the stage for which this stadium, this entire era was constructed in the first place.

The message from the Emirates is that the first of these has already been accomplished. There is a fairly stiff competition for the title of worst walk-off song at the end of a sporting event. But as Sweet Caroline – the thigh-grabber’s favourite and a convincing contender – parped around the stands, as the rain fell in deliciously violent sheets and spurts, as the crowd stayed to laugh and yell , it was hard once again not to feel the change of mood in this previously rather angsty stadium.

The Emirates had been a beautiful sight at kick-off on a cold hard sunlit March day. By the time the darkness fell it was slightly wild. Their former home, Highbury, had something spiky and nasty about it. There is a little of that in this glass and steel mega-bowl now. The away end was drowned out in a way that just never happened in the slow death of late Wenger-ism. “Where’s your fuckin’ VAR?” they sang, in a shared outburst of pointed social commentary. Whatever the future brings, whatever the knotted nature of the club’s hierarchy, you cannot kill the spirit and this place is seething with life these days.

So is the team, in between the odd false step. This game was won on details. Arsenal were a little lucky. Romelu Lukaku might have had a first-half hat-trick. United will move on with the momentum still in their legs. But winning a game in that way, against this kind of team, feels like progress in itself, evidence that, whatever the final level of this team, Emery has already made Arsenal into something they were not.

Victory makes it nine straight home wins in the Premier League, with a real sense of, if not a fortress being built exactly, then a semi-secure gated community. Plus, of course, Arsenal are winning games they approached with fear in their heart until last year. Gone is the collapsible substance of the last few seasons, an Arsenal that fell apart against the better teams like a damp slice of white bread.

Instead Arsenal attacked United with a wiliness in the clinches, the full-backs working furiously, the midfield ferreting hard. It was a game packed with central midfielders of note, from the lesser-spotted Fred, the colossus of Paris; to a rare sighting of Mesut Özil in a major Premier League game, flushed out from his gilded nook on the Arsenal bench like a pedigree chinchilla lured into the light by a piece of cheese on a string.

Özil mucked in and made some nice passes. But it was a less celebrated midfielder that gave Arsenal the lead. It was a weird goal. Granit Xhaka shot from outside the box. By the time the ball crossed the line, just to the left of centre, David de Gea was six feet away from it. Xhaka had spanked through the ball with the top of his foot, slicing it to swerve right to left. De Gea misread the cut, took a step for a swerve the other way and was totally beaten, waving a hand vaguely like a man hailing a rush-hour London bus as it speeds past his stop, windows steamed.

Arsenal took advantage of the moment. Alexandre Lacazette, who had a fine game, took the tumble that won the penalty for the second goal, tucked away by Pierre-Emerick Aubameyang. At the other end Bernd Leno was playing a blinder, making a series of fine saves from Lukaku.

From this point the run-in is as agreeable as these things ever get, with eight winnable looking games to go. It would be deeply Arsenal to trip up now, to lose their way when it suddenly looks clear. But something has shifted here. This might just have been the day when the Emery era found its first real hand-hold.