Kenny defeated Callum Skinner in an all-Britain final on Sunday, Xinhua reported.
He overtook Skinner on the final straight to win the first of their best-of-three races, then showed some veteran poise as he held off Skinner from the lead to make it a clean sweep.
"In London it was one nation only per event so it was a little bit lonely out there. It took me back to Beijing. We've raced against each other so many times in nationals. I suppose there's a bit more on the line here," said Kenny.
Kenny became the second reigning world champion to claim the Olympic crown in this event after British cyclist Chris Hoy at Beijing 2008 Olympics.
"We always feel confident, especially after doing so well in the team events. It's just another race in one way," added Kenny.
Denis Dmitriev of Russia took the bronze by beating Matt Glaetzer of Australia.
"Today I was just going on the track and I just tried to race like an animal with just feeling and instincts, no tactics. I just tried to focus on my goal with my team. I just followed the plan and fought for the medal today," said Dmitriev.
It is Kenny's third medal in this event as he also took bronze at Beijing 2008, and only Hoy who took four medals has won more in individual events in cycling track.
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