Kenny's previous two Olympic gold medals came in the Team Sprint alongside Chris Hoy, but now the 24-year-old is an individual champion after a sensational 2-0 final victory over three-time world champion Gregory Bauge of France.
The Briton qualified quickest for the three-day competition on Saturday and outpaced Bauge in the first of their best-of-three contest.
Kenny then led out the Frenchman and just had too much speed for his opponent to send the Velodrome into raptures.
It was Britain's fifth gold from seven medal events, with the potential for further success on tomorrow's final day of racing.
Australia's Shane Perkins claimed bronze with a 2-0 defeat of Trinidad's Njisane Nicholas Phillip.