Relegated for an illegal move in the second round of the final, Kenny's silver medal in the blue riband sprint capped a bitter-sweet evening for Britain after Laura Trott stormed home to win the omnium at Hisense Arena.
Teenager Trott's triumph brought Britain their fourth Olympic category title at the championships. Australia's gritty sprinter Anna Meares clawed one back for the hosts by winning the keirin.
Kenny trounced Hoy 2-0 in their semi-final, a result that could end the Scottish great's hopes of defending his sprint title at London.
The 36-year-old Hoy beat Kenny for the title at Beijing but only one sprint berth is available per team at London.
After losing the first round, Kenny caught Bauge off guard as he started sprinting from the gate in the second.
The audacious ploy appeared to pay off as Kenny fended off Bauge in a frenzied sprint to the line but replays showed the Bolton-born 24-year-old had edged into the Frenchman's line.
After some hushed minutes of deliberation, Kenny's title was awarded to Bauge, incensing the British camp and sparking some jeering from the packed crowd in the terraces.
Kenny lost the gold medal decider to Bauge at Apeldoorn last year but the Frenchman was stripped of it for failing to comply with the anti-doping "whereabouts" rule.
"It went really well, apart from getting relegated in the home straight," a philosophical Kenny said.
"You can see on the camera I clearly came out of the red (line) fractionally. Whether it affected the outcome of the race is another question. It's not really my place to say."
The decision gifted Bauge his third sprint title and helped erase some of the disappointment of losing last year's gold.
"If you ask me questions about justice, I'll answer you that you have to address them to the UCI," the muscular 27-year-old said, referring to the cycling's global governing body.
"My job is to pedal hard, I'm training every day for it.
"I'm on the road to London."
Chris Hoy recovered to thrash Australian keirin world champion Shane Perkins 2-0 to win the bronze medal and was not ready to concede the Olympic sprint berth to Kenny.
"I'm a little bit disappointed to be honest. I didn't feel I really got the performance I wanted today but that's not taking anything way from Jason or Gregory today," he said.
"You only have to be a fraction off your best and it shows ... Whoever gets the ride for GB at the Olympics in the sprint will do a good job for sure."
Trott struck the early blow for Britain, sealing the six-event omnium in style by winning the final 500 metres time trial leg to edge Australian silver medallist Annette Edmondson for her second gold medal in Melbourne.
The Cheshunt-born Trott, who successfully defended her women's team pursuit title earlier this week, preserved her perfect record of topping podiums at major championships, with her six world and European medals all gold.
Meares, who wept bitterly after arch-rival Victoria Pendleton dashed her sprint title defence in the gold medal decider on Friday, put the disappointment behind her by charging to an emphatic victory in the keirin.
"The crowd ... God, the crowd was great, they got me over it in the end," the 28-year-old told reporters.
"It doesn't make up for last night, it makes today special ... I'm really proud of the way I was able to pick myself up after the disappointment of last night and there's no better way to make yourself feel better than a win."
Russia's Ekaterina Gnidenko took silver and Germany's Kristina Vogel bronze.
Britain have won four of the 10 Olympic category events on offer in Melbourne, with Australia taking three.
Hoy, who hopes to defend his team sprint and keirin titles in London as well as the individual sprint, will bid for the keirin title on Sunday's closing day, the sole remaining Olympic category event at the championships.
Australia's Michael Hepburn upset countryman and defending champion Jack Bobridge to seal the non-Olympic individual pursuit title.
Cameron Meyer lifted the roof with a superb come-from-behind win to seal the non-Olympic points title ahead of silver-winning Briton Ben Swift.