The result takes the Cherries to second on the Premier League table.
Kluivert said afterwards: "Do what I do best and I think I showed that today. As I said previously we have a great team and a lot of great players. I haven't started at the beginning (of the season), I was injured, so it is tough to come into the team again. After a good season for me also, you have to come and show yourself again. And I did that today.
"It's early, but we have to strive for the highest possible. The mentality that we have now is not to look down but up and we will keep doing that. The highest possible and we won't settle for any less, no way."
On Antoine Semenyo's two-goal performance, Kluivert added: "He is incredible. He shows it every game now. He is just world class. We are glad to have him and that is why I said we have a good team. He is the one that scores goals for us and we appreciate that. He's doing an amazing job."