In a thrilling clash that saw both sides finish with 10 men, they could not be separated over 120 minutes, locked at 1-1.
And in a topsy-turvy shootout, Cannes were on the verge of elimination when Saint Etienne's Fabien Lemoine walked to the spot knowing a goal would send his side through.
Lemoine could not add to his side's 3-2 lead though, crashing his effort into the post, before Thomas Lenzini responded for the home side to keep their hopes alive.
Saint-Etienne striker Mevlut Erding then had his penalty saved, allowing Lucas Rouabah to hook his left-foot effort into the top-right corner and spark wild celebrations, as they qualified for the last 32.
A pitch invasion followed as Cannes players and fans embraced following their stunning triumph against Saint-Etienne, who sit fourth in Ligue 1.
Brandao had given the top-flight side the lead after 20 minutes of the match, but Mickael Darnet responded in the 69th minute for the hosts.
Saint-Etienne had Pierre Polomat sent off in normal time, while Cannes substitute Abdel Jamai was given his marching orders in extra time, as the match went to penalties.
Reward for Cannes is a trip to Plabennec, who also play in the fourth tier of French football, in the last 32 on January 23.
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