Briton Kenny saw off the playful Azizulhasni Awang of Malaysia 2-0 in their quarter-final while Bauge overpowered German Robert Foerstemann by the same score.
"It was a tactical race," Bauge told reporters. "I knew him very well. I faced him last year at the world championships. It wasn't easy to manage, but I think I did it well."
Kenny, chosen at the expense of Beijing Olympic champion Chris Hoy to represent Britain as only one rider per nation is allowed in the event, will next face Nijsane Nicholas Phillip of Trinidad and Tobago.
Phillip came out on top of a tightly-contested match with Russian Denis Dmitriev.
Bauge, who beat Kenny in the final to clinch the world title in April, will take on Australian Shane Perkins in a rematch of their world championship semi-final meeting.
Perkins had no problem seeing off American Jimmy Watkins 2-0 as none of the best-of-three matches went to the wire.
The semi-finals and the final will be held on Monday.
Should they prevail, Bauge and Kenny will meet in the final showdown.
"I'm not there yet, but the most beautiful final would be against Jason Kenny," said Bauge.
"He is in front of his home crowd, he will have the pressure. On paper, he is faster since he clocked the fastest time (in qualifying). But tomorrow we start from scratch."
- Jason Kenny