Bennett retained his grip on 10th in the general classification, three minutes 53 seconds behind Froome, with Bevin the next best Kiwi in 84th.
Some of the main contenders for the yellow jersey endured a tough day on the road. Three of the main contenders crashed, as last year's runner-up Romain Bardet (third overall), Jakob Fuglsang (fifth) and twice winner Alberto Contador (12th) hit the deck in separate incidents.
Fuglsang was involved in a crash at the feed zone and went to the medical car to have his wrist checked, while his Astana team-mate Dario Cataldo was forced to abandon, because of a wrist injury, after the Italian also fell.
"He was a key rider," said Astana sports director Dmitry Fofonov. "He would have had an important role in the mountains.
"We have to decide if he undergoes operation in France or in Italy. As for Fuglsang, he already broke the wrist that's injured today - it hurts, he said."
Frenchman Bardet avoided serious injury.
"I escaped unhurt, but now I'm happy that the flat stages are over," said Bardet, who is expected to attack in tonight's 12th stage - a 214.5km trek, featuring three major climbs and a summit finish in Peyragudes.
Contador, who slipped down the general classification after a bad day in the Jura mountains on Sunday, fell off his bike 25km from the finish, but managed to make it back to the peloton with the help of Trek-Segafredo team-mate Jarlinson Pantano.
At that point, the main pack was travelling at full speed, as the sprinters' teams rode hard at the front to catch the last fugitive of the day, Maciej Bodnar of Poland.
After 200km in the breakaway, the exhausted Bora-Hansgrohe rider was reined in 250 metres from the line, before Kittel stole the show yet again.