This was a momentous night in Bournemouth’s history, although the truth is they would have been given a far sterner examination by Coventry or Hull. You can only beat what lies in front of you and Marco Rose’s players never relinquished control against a rotten impersonation of a Milan side. The visitors resembled holograms even before Mike Maignan, their goalkeeper, rendered their task impossible with a deserved sending-off in the first half.

By then Justin Kluivert had given Bournemouth the lead with a penalty and it was another spot-kick from Marcus Tavernier, given after Maignan’s rush of blood, that underlined their overwhelming superiority. Amine Adli applied the garnish with a late free-kick and it meant an abject return to British shores for Ruben Amorim, who would have been excused seeing this particular week as the opportunity to make a point. On this evidence Manchester United, to whom Bournemouth travel on Sunday, share more than a few similarities with the modern version of Milan.

At kick-off the local and broader contexts were impossible to ignore. Bournemouth could hardly have imagined, making their great escape from the fourth-tier trapdoor in 2009, that their modest home would host such a luminous name in a competitive fixture. On the weekend they beat Grimsby, the Rossoneri were overcoming Palermo thanks to goals from Kaká and Filippo Inzaghi. However hard you squinted, seeing the seven-time European champions’ colours on display here felt a trick of the light.

“How did we end up here?” asked the public address announcer, a question repeated on a banner hoisted by the north stand. It was worth posing with a bigger picture in mind too. After all, what has happened in football’s ecosystem to ensure the Premier League’s 15th-placed team, for all their merits, could justifiably be named pre-match favourites against one of the most decorated institutions in Serie A?

Sheets of swirling, driving rain were packaged in the south coast welcome for Amorim. He braved the elements without recourse to hat or hood; England had, perhaps, left him more bedraggled in the past. But within eight minutes he suffered a further dampener when, after a rapid Bournemouth start, Kluivert converted from the spot.

The scorer had been involved in a close call directly beforehand, failing to apply contact after fine work from Evanilson and seeing Ben Gannon-Doak’s strike deflected wide as the ball ran on. Milan did not clear their lines from the resulting corner and were punished when VAR found Koni De Winter had deflected Evanilson’s header wide with his arm. There could be no complaints for Amorim.

Bournemouth, whose colours were derived from those of Milan in 1970, continued to force the pace. Yunus Musah was dispossessed and Ryan Christie forced Maignan into a save. When one of Milan’s three Englishmen, Omari Hutchinson, tried to profit from a loose Gannon-Doak pass he could only run into António Silva.

Unlike most of his teammates, Hutchinson at least looked capable of matching Bournemouth’s intensity. Overall Milan could not cope and before the half-hour they self-destructed dramatically. It was a moment of supreme idiocy from Maignan, who had just clawed James Hill’s deflected strike wide but elected to shove Tyler Adams in the face as the subsequent corner was sent in. The penalty award was clear and so was the red card shown to Maignan.

Hutchinson was sacrificed for the replacement keeper Lorenzo Torriani, who was quickly beaten. This time Tavernier, unfazed by a lengthy wait, did the honours in style. An easing-off of the downpour before half-time was scant comfort for Amorim.

Adrien Rabiot was introduced at the break for Milan, whose best hope now was that Bournemouth fancied keeping something in reserve. Their right wing-back, Diego Moreira, bustled forward in a rare suggestion of appetite but it was Gannon-Doak, on the other side of the pitch, who threatened more consistently with a series of darts to the byline.

The wind had swelled to the extent that an Ardon Jashari free-kick, aimed from just inside Bournemouth’s half, blew back towards him before reaching the box. Bournemouth had no need for such help from the elements. They were hardly assisted in their quest for a third by the referee, Vasilis Fotias, who pulled play back to book a lumbering Fikayo Tomori for a foul when the substitute Lewis Cook was clean through.

Christie sliced wide before Adli, a substitute, curled in delightfully from 22 yards. Bournemouth’s faithful could sing in the rain to their heart’s content.