At £15 a pop, the half-and-half scarf sellers outside of the Vitality Stadium were cleaning up, and while those souvenirs are often derided as cringe fodder for tourists, there was no blaming those Bournemouth fans queueing to buy one this time.

On the one half, Bournemouth, a club beaten 2-1 at home by Bury in League One 15 years ago on this night. On the other, AC Milan, the Italian behemoths and seven-time conquerors of Europe.

It was only once inside the Vitality that those supporters found a free scarf awaiting them courtesy of their club, reading: ‘We are all going on a European tour.’ Not to worry. They would happily take multiple mementoes from this – the night AFC Bournemouth famously flattened AC Milan.

There was a special feel to it all, from the fireworks exploding over the Vitality to the playing of Andy Williams's The Impossible Dream to the enormous tifo reading: ‘How did we end up here?’

A few in the Milan end may have been asking themselves the same, especially when their once-great team was trailing 1-0 after eight minutes and 2-0 after 32 in this Europa League fixture.

Both of those goals were penalties – Justin Kluivert scoring one and Marcus Tavernier the other – while Milan then spent the remainder of this match playing with 10 men as their goalkeeper Mike Maignan was red carded for shoving Tyler Adams in the face.

By the end, when Amine Adli delivered the coup de grâce with a 25-yard free-kick, Ruben Amorim could only laugh. Literally, the former Manchester United manager now in charge of Milan chuckled as Bournemouth’s supporters serenaded him with: ‘Ruben Amorim, it’s happened again.’

Considering one Italian journalist in the press box angrily ripped his accreditation to smithereens as the visitors trailed 3-0, Amorim’s smiling response may not go down too well back home.

Yet our newspaper counterparts from Italy saw this coming. They were wearing a told-you-so look after it all, having warned us this would happen. ‘You don’t understand,’ one said when asked before kick-off. ‘This isn’t the AC Milan of old.’ Indeed it is not, and Amorim tried to hide behind Maignan’s dismissal afterwards: ‘We need 11 players on the pitch at all times. We killed our game.’

Bournemouth boss Marco Rose added: ‘Our club, we stay humble. We know we are good. If we have the whole squad, we know we can compete with anyone, anywhere. But the season is long. We have so many games. Sunday, Wednesday, Sunday. It’s so demanding.’

Bournemouth might not have even existed were it not for their former chairman Jeff Mostyn, who was here as a fan, writing another £100,000 cheque to save them from liquidation in 2008.

This represented a major milestone for them in their first-ever season in Europe, and while Bournemouth were happy to embrace this as extraordinary on this occasion, they want these nights to become the norm. Their owner, Bill Foley, is striving for that and victories like this cannot hurt show their better players such as Chelsea target Alex Scott why this club is no stepping stone.

Bournemouth won here even without the injured Scott. Rose’s side took the lead when Evanilson headed Tavernier’s cross, but Koni De Winter handled the ball on its way wide. Nobody in the stadium noticed it, but VAR Dennis Higler of the Netherlands did, and then referee Vassilis Fotias of Greece did, too, via his monitor. Kluivert rolled the ball into the bottom-right corner for 1-0.

Amorim’s anger with his players was already rising in the technical area when Maignan pushed Adams in the face at a Bournemouth corner. The whistle was blown. Again, hardly a soul in the crowd knew what was happening until Maignan was shown a straight red card.

Needing to bring on replacement goalkeeper Lorenzo Torriani, the unfortunate one sacrificed was Omari Hutchinson, the 22-year-old whose shin pads carry a picture of himself representing England’s Under 21s. A new taker in Tavernier made it 2-0.

Adli’s free-kick in the 84th minute capped this victory with Milan ending the match without a single shot on target. Even with 10 men, that was an embarrassing statistic.

This was a night to cherish for Bournemouth, now winners in all three of their Europa League outings. Indeed, a fair few will hang those scarves in their homes as a reminder. But as a club aiming to go places, they hope this is just the first of many matches with European heavyweights.