The Ag2r-La Mondiale rider dragged himself over the line, rain soaked, after a summit finish to claim stage eight, a 161-km trek from Tomblaine to Gerardmer La Mauselaine, with a solo breakaway. Nibali retained the yellow jersey by finishing third, three seconds behind Alberto Contador.
Two-time Tour winner Contador (Team Tinkoff-Saxo) attacked several times on the last ascent and the Italian could not respond to the last acceleration after Astana team-mate Jakob Fuglsang was dropped in the final climb.
"Alberto Contador took the race in hand. The last climb suited him more than me," Nibali said. "It was very difficult and explosive. We've all paid for the efforts of the previous days."
Yvon Madiot, sports director of the FDJ.fr team, agreed the first week of racing had been extremely demanding. "The Tour will be long for many good riders. I saw a lot of good riders very tired," he said.
American Andrew Talansky, who crashed on Friday, hit the tarmac again on the slippery descent from the Col de la Grosse Pierre with less than 10km to go. The Garmin-Sharp rider lost more than two minutes to Nibali and Contador, dropping to 16th overall.
Australian Richie Porte, promoted to Team Sky leader after the loss of Chris Froome, finished fourth in the stage ahead of French hope Thibaut Pinot. Porte is third overall, one minute 58 seconds behind Nibali, with Dane Fuglsang in second place 1:44 off the pace. Contador is sixth, 2:34 adrift of Nibali, and just behind fellow Spaniard Alejandro Valverde (Movistar).
It was a positive day for Porte, who said: "I'm happy with how that went. It is not really my bread and butter and I think that on the longer climbs I will be better."
He acknowledged that the aggressive riding of Contador's team had changed the landscape, though. "Tinkoff Saxo are riding very aggressively from a long way out, a bit like Team Sky used to do," he said.
Nibali insisted the race would not become a straight battle between him and Contador. "The race is not a duel, it's more than that. Richie Porte is up there," the Italian said. "He's not here by co- incidence. I've also seen Valverde riding with ease. There have been great riders in action today."
Kadri was part of a five-man breakaway that also included Britain's Simon Yates (Orica-Green Edge. Kadri attacked on the first climb of the day, 25km from the finish, and never looked back as he took the polka-dot jersey as the leader in the mountain classification. Yates battled gamely but was eventually eaten up by the peloton.
"Our goal as a team was to win a stage. The polka dot jersey is the icing on the cake," said the Bordeaux-born Kadri, 27.
Today's ninth stage should be quieter for the top guns. It is a 170-km run from Gerardmer to Mulhouse that is likely to see the breakaway specialists in action.