The British partnership dominated the 120-lap race inside the Izu Velodrome, finishing with a phenomenal score of 78 points to end well clear of second placed Denmark on 35 and the bronze winning Russian Olympic Committee on 26 points.
This outstanding achievement added to Archibald's team pursuit silver medal won earlier in the Games, while Kenny became the first British woman to win golds at three consecutive Olympics.
Archibald, 27, who also landed a team pursuit gold medal at the 2016 Olympic Games in Rio, said: "I've been dreaming about this.
"I've never wanted something so much and I've never been so nervous. But we've been clinical in our approach.
"I'd like to thank our coach Monica (Greenwood).
"None of this would have happened without her as she overhauled our approach to this event."
Archibald and Kenny looked in command from the start, winning the opening three sprints on the track and then further increasing their lead after the Dutch pair of Kirsten Wild and Amy Pieters, current world champions, were caught in a crash with just over 70 laps left.
In the second half of the contest, the British duo got themselves in a series of breakaways, scooping points in the sprints and gaining a lap with just over 20 to go to build an all-but-unassailable lead.
By the end of the race, they had won 10 of the 12 sprints - including the double points for the last lap - to finish with 78 points, more than twice the tally of second-placed Denmark on 35.
Kenny, the first British woman to win golds at three consecutive Olympic Games, said: "It's unbelievable. I am just so glad.
"I've never wanted to win a race so badly in all my life. That was the one. I messaged Jason (her husband) this morning and said: 'I feel like my Olympics ends today'.
"The one race I really wanted to do was this and we went and did it.
"I couldn't have done it without these girls.To have Katie there the whole time, I just feel like I'm racing with a sister and I couldn't have done it if we didn't have that relationship."