Sochaux, who are 10th in the league, struggled against fifth division Chambery after demolishing top-flight title outsiders Stade Rennes 5-1 at the weekend.
The visitors went in front through striker Brown Ideye in the 21st minute but Chambery, who also beat Brest and Monaco in the previous rounds, rallied with two second-half goals.
"This reversal of fortune, it was incredible," goalkeeper Guillaume Bemenou told Eurosport. "At half-time our coach (David Guion) told us we could not die like that without playing our football."
Fabien Tissot-Rosset, who installs kitchens for a living, equalised just after the hour with a volley from a free-kick and Aissa Yahia Bey, a sports educator, grabbed the winner midway through the second period with a powerful 30-metre strike.
In the dying minutes, Bemenou produced a string of saves to thwart Sochaux.
"It's magnificient, extraordinary!", defender Stephane Roux cried. "The crowd... it's amazing. Tomorrow I'm telling my boss I'm sick, I'm going to party." Roux works as a delivery man.
"We were sleeping for half an hour in the second half," said Sochaux coach Francis Gillot. "We woke up in the last 15 minutes but it was too late."
France striker Guillaume Hoarau shone for holders Paris Saint-Germain, hitting a hat-trick in a 4-1 demolition of fourth-division Martigues.
"We needed to do the job," Hoarau said. We remained professional until the end. It is not always easy to face amateur clubs because they are playing the match of their life."
Ligue 1 leaders Lille squeezed past second-division Nantes 3-2 on penalties after a 1-1 draw but top-flight Nancy came unstuck at home to Ligue 2 Le Mans, losing 2-1.
