Kluivert opened the scoring from the penalty spot in the eighth minute, with Marcus Tavernier converting a second spot-kick before half-time. Amine Adli then sealed the result with a fine free-kick in the closing stages, giving Marco Rose’s side nine points from nine in the Europa League.
For Kluivert, the result reflected a belief that Bournemouth can compete regardless of the opposition.
“I think it means a lot,” he said. “We come from two victories, so that gives us a good feeling for this game.
“What we say is we just trust in ourselves. It doesn’t matter who we play against, we trust in ourselves. We know what we’re capable of, and I think we showed that tonight again.”
Milan’s task became considerably harder when goalkeeper Mike Maignan was sent off in the 27th minute for pushing Tyler Adams in the face. But Kluivert was keen to recognise the stature of the opposition and the significance of beating a club with Milan’s history.
“AC Milan have a lot of history, it’s a great club, a big club,” he said.
“What I’ve heard, which I didn’t know before, is that we have comparisons. The colours that we have, the red and black, come from AC Milan, so it’s nice for those things. It was a big game tonight and we won it.”
Bournemouth have now won three consecutive Europa League matches without conceding, and Kluivert wants the team to maintain those standards as the schedule continues.
“We know the run that we have now, three wins, no goals conceded,” he said. “It’s something that I’m proud of. We need to continue, and we know how we can continue, we have done it before.”
The forward also believes the competition for places will help Rose’s squad as players return from injury.
“We have a nearly fit squad now, and other guys are coming back,” he said. “Competition makes us better.
“The thing I love about our team is the intensity that we have. It doesn’t matter who is in the starting 11, our intensity shows who we are and what we stand for. It doesn’t matter who plays, we always go full gas.”
Kluivert’s willingness to share responsibility was also evident from the penalty spot. After converting the first, he allowed Tavernier to take the second.
“I’ve got to be generous, I’ve got to give my teammates a good feeling,” he said. “They deserve to score a penalty as well, because I know they can score a penalty too.
“That also shows that we are a team and not individuals.”
For Bournemouth, that collective attitude has accompanied a perfect start in Europe and a memorable victory over one of the continent’s most decorated clubs.