The Blues, who had lost their previous three matches before the World Cup to slip out of the top six, swept Bournemouth aside thanks to early goals from Havertz and Mason Mount.
“I was delighted to score but the main thing was to get the win and that’s huge for us,” Germany frontman Havertz told the club 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.
“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 handed the central striker’s role by head coach Graham Potter and grabbed a superb poacher’s goal by sliding in to convert 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,” he added.
“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.
“He gives me a lot of confidence and I really enjoy working under him.”
Mount’s 20-yard curler all but killed Bournemouth off with just 24 minutes on the clock, but manager Gary O’Neil took the positives from a spirited second-half display.
“If we perform like we did for the second half, especially, we will cause teams problems,” he said.