The Dutchman netted all three spot kicks won by striker Evanilson, seemingly beating goalkeeper Jose Sa with ease with each.
In doing so, Kluivert became the first player to score a hattrick of penalties in the Premier League, while his teammate is the first to win three in the league.
Speaking after the game on this record, Kluivert said: “That sounds beautiful. Because to go into the history books, that's amazing, I’m super happy with it.”
Each spot kick was different.
For the first, Kluivert waited for Sa to move before finishing confidently down the middle as the keeper dived out of the way.
The second, he smashed past the keeper who was left with no chance, despite diving the right way.
Kluivert again waited for Sa to make the first move, before slotting home and wheeling away to celebrate his hattrick.
(Image: Nick Potts/PA Wire) Speaking on each penalty, Kluivert said: “I trained them, we have a great keeper with Kepa.
“I trained them and we tried some stuff.
“The first one I stopped, so I look at the keeper, what he's doing, and then I want to switch it up for the second one.
“And the third, he doesn't know what I'm going to do. Am I going to shoot it straight away or am I going to wait?
“Then I try to stay composed and he chooses for me. As easy as that.”
Asked what he would be doing with his match ball, he said: “[I’ll] put it in my daughter's room for her to come in February and she can see how her dad did it in football.”
On the Cherries performance as a whole, Kluivert said the side’s high pressing and direct play, particularly in the opening period of the game, is a ‘key factor’ in how the team plays.
(Image: Nick Potts/PA Wire) “If we do that how we did it today and we showed a lot of teams how we can do that, I think what we have shown, we can beat a lot of teams in this league,” he said.
“So I'm happy that we've done it like this today also.”
The other goal scorer on the day for Bournemouth was left back Milos Kerkez.
In recent weeks, Kluivert has been honing his barbering skills by cutting the Hungarian’s hair – and he said it was no coincidence that in that time, Kerkez has started adding assists and now a goal to his game.
Kluivert laughed and said: “I think after me cutting his hair, he's giving assists, scoring goals.
“So yeah, he doesn't want another barber, so I'm going to up my price also!”