In the second semi-final, Bauge was able to round Australia's Shane Perkins and win by half a bike length to take a 1-0 lead. The Frenchman then held off Perkins in the second bout to advance.
The one rider per nation rule introduced by the International Cycling Union and International Olympic Committee weakened the field and saw Kenny selected ahead of 2008 winner Sir Chris Hoy, but a Kenny versus Bauge final was befitting of the blue riband event.
Kenny finished second to Hoy in Beijing and to Bauge at April's Track Cycling World Championships in Melbourne.
The Briton was awarded the 2011 world title after Bauge was stripped of the rainbow jersey for an anti-doping infringement.
In the corresponding women's event, Victoria Pendleton eased to a comfortable victory in the first bout of her best-of-three quarter-final with Olga Panarina of Belarus.