Germany moved eight points clear of second-placed Romania, who beat Armenia 1-0 on Monday, with two games to play.
“We now have five wins from five this season,” Germany boss Hansi Flick said.
“You have to compliment the team on their attitude. Of course the first half was a bit wild, but we can be happy that we won and qualified.”
The four-time champions failed to get out of the group phase at Russia 2018, while Joachim Low’s rein came to an end at Euro 2020 when they lost to England in the last 16.
Havertz added: “Things are definitely going in the right direction. We played confidently here and the last few games have shown the quality we’ve got.
“It was important for us to go into World Cup qualifying well, especially after the Euros, which was disappointing for us. Now we’ve qualified, which is very important.
“Our aim is to win the World Cup. When you play for Germany the objective is always to win titles. That’s the approach we’ll take when we go there next year, but there’s still a very long road ahead.”
Other European nations close to securing qualification include Denmark, Belgium, the Netherlands and England.