Kenny and Archibald, now a two-time Olympic champion, won 10 of the 12 sprints to finish on 78 points, 43 clear of Denmark, who took silver.
The Russian Olympic Committee took the bronze with 26 points after 120 laps of the Izu Velodrome.
It was Kenny's first Olympic gold since giving birth to her son Albie in 2017 and she said she considered quitting the sport during the pregnancy.
"When I fell pregnant, there was a moment two months into the pregnancy where I woke up and said to Jason (Kenny, her husband), 'I can't do this, I'm not going to be able to carry on (with cycling), there's just no way'. And here we are," she said.
Kenny's sixth medal overall draws her level with dressage rider Charlotte Dujardin as Britain's most-decorated female Olympic athlete.
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