The Blues, who had lost their previous three matches before Qatar 2022 to slip out of the top six, got back on track on Tuesday as early goals from Havertz and Mason Mount saw them ease past the Cherries at Stamford Bridge.
"I was delighted to score but the main thing was to get the win and that's huge for us," Havertz told Chelsea's website.
"The win and the goals will hopefully give us confidence going forward. We lost three before the World Cup break so it was important we got the victory in the first game back, so we are very happy to do this."
The German international added: "We have to keep winning and this period coming up is going to be crucial for us.
"We are going to give our best in the next games to get on a run and this is a fantastic start for us."
Havertz was given a central striker role by Chelsea boss Graham Potter against Bournemouth and proved himself at home in the position as he slid to turn in Raheem Sterling's cross.
"I know the vision that Raheem has and he likes to play those sort of balls. It was the perfect pass to me, with the right weight on the cross," Havertz said.
"I was in the right position and I was very happy to score.
"The coach gives me the freedom to do whatever I like on the pitch and I like to be expressive on the ball, so it's good.
"I like to play free and to get into the box and he's told me to do that more, so I was happy that it paid off with the goal."
However, victory came at a cost with Reece James limping off with a recurrence of a knee injury that saw him miss out on England's World Cup campaign.
In a statement, Chelsea said James will be sidelined for up to a month and the right-back admitted his mental health has suffered due to his injury problems.
"2022 has been the toughest year to date," James said on Twitter. "Just wanna thank you all for the support, none of you go unnoticed.
"It's naturally affected me mentally, I'm currently just trying to deal with the cards I've been dealt. I hope your end of year is filled with peace, joy and happiness."
James sustained his initial knee problem in October during a Champions League fixture with AC Milan.
Meanwhile, Chelsea made their first move of the January transfer window on Wednesday with the signing of striker David Datro Fofana from Molde.
The Ivorian international, who scored 24 goals in 65 appearances for the Norwegian club, will officially join the Blues on New Year's Day.
Fofana will add depth to Potter's options up front after Armando Broja was ruled out for the rest of the season with an anterior cruciate ligament injury.
"Fofana has previously revealed that he wanted to follow in the footsteps of Chelsea legend Didier Drogba, and that the Premier League was his big dream," Molde said in a statement. "Now the dream is coming true for the youngster."
