He did it in front of his home crowd and on the sport's biggest stage to win track cycling's marquee event in supreme fashion and extend Britain's ruthless domination at the London Velodrome.
Kenny gave the British track cycling squad its fifth Olympic gold medal out of seven possible after outclassing Bauge in the final of the men's sprint Monday.
The 24-year-old rider from the northern English city of Bolton could not have dreamt of a better scenario for his maiden win against the three-time world champion, living up to huge expectations and making good on the British team's decision to enter him in the event instead of defending champion Chris Hoy.
"I just thought, 'If Chris is in my shoes, there's no way he loses this one.' It was just about justifying my place," Kenny said after dispatching Bauge with a 2-0 win in the best-of-three final.
"It felt amazing. It feels a bit surreal. It hasn't sunk in yet, getting dragged here, there and everywhere."
Kenny was awarded the sole spot available for the British team after the sport's governing body changed the competition format to allow only one rider per nation in the sprint.
Kenny raised his arms aloft after crossing the finish line as the velodrome erupted in cheers and applause. Kenny, gold medallist with the sprint team last week, then seized a Union Jack flag and brandished it before the crowd.
He was also a member of the British team that won gold four years ago in Beijing in the team sprint.
Kenny got off to a perfect start in the final after starting on the outside of the track. Bauge watched him closely during the first lap and prevented him from going past on the inside, but was still overpowered in the home stretch.
In the second leg, Kenny led from the start as Bauge vainly tried to catch him in the final sprint.
"It's always nice to finish it in two, especially if you feel you're faster," Kenny said. "I just wanted to take the race from him and that's what I did. I raced him in the world championship finals the last two years, and both times he was slightly faster. I worked hard the last six months to close that gap."
Shane Perkins claimed the bronze medal with a 2-0 win over Njisane Nicholas Phillip of Trinidad and Tobago.
Bauge failed in his bid to become the first Frenchman to win the Olympic sprint title in 40 years and looked devastated afterwards.
"It's a huge disappointment," he said. "It was the final I dreamt of, against an Englishman. I lost in two legs, but I did not make any mistake. I was in a good shape, I was not afraid and well prepared. He was just better and the crowd gave him an extra something."
Kenny claimed his second gold in London after winning the team sprint with Hoy and Philip Hindes last week. He was under intense pressure to justify being picked ahead of Hoy — who was awarded a knighthood after winning three golds in Beijing.
He got off to a bright start in the tournament, showing his credentials in qualifying by posting the best time in a new Olympic record.
In the final, he kept his head cool and was in complete control.
"I really didn't get to enjoy the team sprint," he said. "I felt a little sick, so I let the rest of the guys celebrate while I tried to keep my lunch down. It was nice this time to enjoy the moment."
With Kenny's win, the host country equaled Italy's 22 gold medals in the sport. Only France has won more gold medals in track cycling, with 28.
Kenny, who was second behind Hoy in Beijing, became the first British man to win two medals in the event at the Olympics.
Bauge, who in January was stripped of the gold medals he won at the 2011 worlds for a violation of anti-doping rules, had easily defeated Perkins in the semifinals while Kenny had progressed with a 2-0 win over Phillip.
"I'm tired of finishing runner-up," Bauge said, referring to his silver medal in the team sprint. "I was born to win. But Kenny raised his level, as all his teammates here. We need to work on the small details that help them to achieve such great success."
The sport's governing body, UCI, annulled Bauge's victory in the individual sprint event and the gold medal he helped the French win in the team sprint race at the 2011 worlds after the French federation imposed a one-year backdated suspension on Bauge for violating rules on rider availability for drug tests and for one missed test in 18 months.
Kenny, who has been described by Hoy as the future of cycling, was awarded the 2011 sprint world title after Bauge's disqualification.
But the Frenchman, who has won the world title three of the last four times, beat Kenny in this year's final at the worlds in Melbourne, Australia.
There, Kenny tried to surprise Bauge by attacking from the start in the second leg, but was relegated for moving out of his lane. On the Siberian pine wood of the London Velodrome, he was simply too fast and did not need such tactics.
Kenny's superb performance left France coach Florian Rousseau a bit perplexed.
"Kenny was exceptional today and Greg can be happy with his race," Rousseau said. "I can't explain why the British team is so strong. It's maybe because there are only the Olympics which matter to them. But we have the same approach. I don't want to stay stupid things, we just need to think about it and come back with the right answer."
AP Sports writer Dave Skretta contributed to this report.