AG2R rider Bardet, 24, beat a breakaway group to the top of the 1,924m Col du Glandon and, with 34km remaining of stage 18, eked out a decisive lead.
Pierre Rolland finished 33 seconds behind to complete a French one-two.
Britain's Froome stays three minutes 10 seconds ahead of Colombia's Nairo Quintana with three stages remaining.
As happened during stage 17, 30-year-old Froome and Team Sky withstood several attacks on the 186.5km route from Gap to Saint-Jean-de-Maurienne.
But there was little panic among Froome's disciplined team, and the Team Sky leader looks confident of repeating his triumph of 2013.
Alejandro Valverde remains third with Team Sky's Geraint Thomas, 29, fourth.
