Rasovszky timed 1hr 50min 52.7sec to finish just over two seconds ahead of Germany's Oliver Klemet in the race on the River Seine.
The Hungarians had trained extensively on the Danube in their homeland ahead of the rare race on the river rather than the more typical lake contest and that proved to be a smart move.
"I think it was really good preparation in how to swim a river and gave us a good advantage to know where and how to swim in the Seine," said Rasovszky.
Rasovszky, the reigning world champion and silver medallist from Tokyo three years ago, took the initiative early, grabbing the lead on the second lap.
The 27-year-old exchanged the led with German Florian Wellbrock, the defending champion, but then emerged on top from that duel, grabbing the lead decisively at the 6.6km mark.
While Wellbrock faded, finishing eighth, Klemet took up the challenge for Germany and pulled away from the pack to chase down Rasovszky.
But the Hungarian, nicknamed 'The Balaton Shark', had the energy and the tactical nous to hold on to his advantage towards the finish at the Pont Alexandre III bridge.
"I really like swimming out front and it paid off for me in Doha at the world championships, I led there also for most of the race. I knew it was almost impossible to overtake against the current, so I new if I could reach the turn for the last lap in front, it would give me a great chance," said Rasovszky.
Compatriot Betlehem delivered a late burst to pip Italy's Domenico Acerenza to third place and praised Hungary coach Laszlo Szokolai for the team's preparation on the river near the town of Szazhalombatta.
"I'm very proud of myself and Kristof and also Lazio because it was his idea and he made it possible for us to swim there," he said.
The race, with the backdrop of the Eiffel Tower, had been at risk due to concerns over the water quality and the possible impact on the health of the swimmers.
Betlehem's girlfriend Bettina Fabian had finished fifth in Thursday's women's event however and told the team that the water had been fine.
"So I thought, OK, no one is going to care about the water now, we just need to race and win a medal. Maybe afterwards we have to drink some Hungarian palinka (fruit spirit)," he said with a grin.
Klemet, who finished seventh in the men's 400m freestyle in the Paris pool,was delighted to have a medal from open water.
The German was a bronze medallist in the 10k event at the Fukuoka world championships in 2023.
"It means everything. We trained the whole season for it and the last three years since Tokyo. I just wanted to win a medal here.
"We focused more on the open water because the chances were higher to win a medal. We did a good job analysing the venue and the current and it paid off," he said.
