Livano Comenencia levelled the game 1-1 with a left-footed strike in the 21st minute to give Curacao their first goal in the tournament and send fans of the tiny Caribbean nation into a frenzy.
But it was all Germany after that with the four-time champions regaining the lead on Nico Schlotterbeck's header off Nathaniel Brown's corner kick in the 38th minute.
The margin of victory comes well short of the World Cup record of nine goals, which has happened three times, the last coming when Hungary saw off El Salvador 10-1 in 1982.
Havertz converted from the spot in first-half stoppage time to make it 3-1. after Germany were awarded a penalty shot when Felix Nmecha was tripped by Riechedly Bazoer.
And Germany wasted no time after half-time to extend the lead with Jamal Musiala netting in the 47th minute, Brown making it 5-1 in the 68th and Deniz Undav adding a six goal before Havertz's second goal came in the 88th minute.
Germany head coach Julian Nagelsmann said: "It took us a few minutes to get back into the game after they equalised. Curacao can play football too, as we saw, and I'm curious to see how they'll fare in the group going forward.
"I'm very satisfied with us scoring seven goals and our performance for the most part. A winning start is always important and we're glad we managed it."
The crowd of 68,021 inside NRG Stadium was overwhelming rooting for Germany, but there was a spirited contingent of people cheering on Curaçao as it became the smallest country to ever appear in the tournament.
Manuel Neuer, the 40-year-old goalkeeper who came out of international retirement for the tournament, had one save in his first appearance for Germany in almost two years.
The match featured the largest age gap between coaches in World Cup history with Curaçao's 78-year-old coach Dick Advocaat becoming the oldest ever in the tournament against 38-year-old Julian Nagelsmann, who is the youngest coach in this year's tournament.
Germany face Ivory Coast in theirnext match in Toronto on Saturday while Curacao take on Ecuador in Kansas City on Saturday.