The 2023 world champion came from behind to touch out in one minute 54.26 seconds, 0.56 ahead of Greek silver medallist Apostolos Christou, at the La Defense Arena.
Switzerland's Roman Mityukov the bronze.
Christou led for the first 150 metres, with Kos then slotting into second at the 150 mark before moving up a gear to power past.
Kos has been working with Michael Phelps' former coach Bob Bowman, who is also training France's triple gold winner Leon Marchand.
"I just kept swimming and swimming and you know, I was just happy to get my hand on the wall first," said the Hungarian.
"It was just a different race strategy today. I just knew that I have to do something like that to win. It doesn't really matter how I got there. The point is that I got there and I'm just really happy."
The last Greek swimmer to win an Olympic medal was Spyridon Gianniotis who finished second in the 10km open water marathon in Rio de Janeiro in 2016.
Greece has otherwise not taken a men's medal in swimming since the Athens Games of 1896.
