The Cherries bounced back from consecutive defeats to claim a 4-2 victory over a Wolves side managed by former Bournemouth boss Gary O'Neil.
Bournemouth's successful outing was made even sweeter by the fact that two of their players created Premier League history at Molineux.
Kluivert showed great composure from 12 yards to score a hat-trick of spot-kicks, becoming the first player to net three penalties in a single Premier League game.
Evanilson, who joined Bournemouth from Porto in the summer, won all three of the penalties, etching his name into the history books as the first individual to win three penalties in a single game in the competition's history.
Kluivert reacts to "amazing" feat
Speaking after his first Premier League hat-trick, Kluivert admitted it was "beautiful" to create history with his three spot-kicks.
"That sounds beautiful, to go in the history books. That is amazing. I'm super happy with it," Kluivert told Premier League Productions. I train them [the penalties].
"We have a great goalkeeper, Kepa [Arrizabalaga]. We try some stuff. The first one, I stop and look at the keeper, what is he doing? I switched it up for the second one.
"Then the third one, he doesn't know what I'm going to do. I waited and he chose for me. Easy as that. We have shown that we can beat a lot of teams in this league. I am happy."
Iraola heaps praise on Evanilson
Evanilson was unable to add to the four goals he has scored this season, but he still managed to have a decisive influence on the contest.
Bournemouth boss Andoni Iraola took the opportunity to praise the Brazilian striker as well as commenting on Kluivert's confidence from the penalty spot.
"Evanilson has made the difference today," Iraola told BBC Match of the Day. "He has been fighting with the centre-backs and the goalkeeper. He was phenomenal.
"Justin [Kluivert] has played against my teams in Spain many times, and has also scored penalties. Justin is normally quite confident in those situations.
"The first two were clear. For the third one, I thought maybe he is not the one to take it. But also, in the moment, I didn't want to be the one to tell him. Every time you take another penalty, it becomes more difficult because you are giving the goalkeeper more information.
"But I would also like to acknowledge Evanilson. He didn't score today but he is [the reason] why we won."
After claiming their second away win of the Premier League season, Bournemouth will now turn their focus to Thursday's home match against Tottenham Hotspur.