The 21-year-old struck in the 42nd minute to give underdogs Chelsea a deserved victory, instantly repaying a large chunk of the club-record £72 million ($102.23 million) his signing cost the club when he joined from Bayer Leverkusen last summer.
Havertz scored his first-ever Champions League goal, racing on to Mason Mount's superb through ball and evading the out-rushing City keeper Ederson before calmly rolling the ball into an unguarded net.
"I don't know what to say. I really don't know what to say. I waited a long time," Havertz said on the pitch.
"I've waited 15 years for this moment and now it's here."
Havertz's lack of form was one of the reasons Frank Lampard was sacked as Chelsea manager in January, by which time the player had managed only one Premier League goal. Even when fellow German Thomas Tuchel took over, the forward continued to struggle for form and did not manage another goal in the league until April. But under Tuchel, Havertz has slowly begun to show the skill that made him such a target for Europe's biggest clubs.
"He deserves that, it's been a tough season," said Chelsea skipper Cesar Azpilicueta, hugging his teammate as the celebrations got going on the pitch.
"This guy is going to be a superstar. He is already. He gave us the Champions League and not only that he ran like crazy."
Information from Reuters was used in this report.