London 2012 champion Kenny came out on top in the first two races to win the best-of-three final.
Russia's Denis Dmitriev beat Australia's Matthew Glaetzer in the race for bronze.
Britain’s Kenny, 28, has now won as many Olympic golds as rower Sir Steve Redgrave and fellow cyclist Sir Bradley Wiggins.
Only Sir Chris Hoy, also a cyclist, has won more with six but, Kenny can still beat Hoy’s record when he races in the Keirin on Tuesday.
In a report, Kenny told BBC that the win was so special Kenny told BBC Sport.
"I'm really grateful, everyone works so hard for us. When we win it feels like the team is winning and we have everyone behind us, pushing us."