Oh defeated Farès Ferjani of Tunisia in the final bout to become the first Korean man to win gold in the event.
With Saturday's victory, Oh became the first Korean fencer to achieve the feat of winning at four different major competitions -- the Olympics, the Asian Games, the World Championships and the Asian Championships.
Kim clocked in at 3:42.50 to finish third. Germany's Lukas Maertens won gold with a time of 3:41.78 after leading the entire race while Australia's Elijah Winnington secured silver with 3:42.21.
Korea wrapped up the first day of the quadrennial sporting event, with three medals - one gold, one silver and one bronze.