The Briton’s bike was broken in a pile-up close to the finish and the Team Sky rider began running up the slopes of Mont Ventoux before grabbing a service bike which did not work.
Froome was then given a spare Team Sky bike on which he completed the 178km stage, losing more than a minute to his main rivals, only for the race jury to rule that he would be credited with the same time as the two riders he was with when the incident occurred.
“Chris Froome and Richie Porte have been given the same time as Bauke Mollema due to the incident in the finale. Froome retains the yellow jersey,” organisers said.
BMC rider Porte, who was leading Froome and Dutchman Mollema (Trek Segafredo), crashed into a TV motorbike that was held up by the crowd on the road.
Mollema and Froome also tumbled and the Briton’s bike was broken in the incident.
The overall lead was first handed to Briton Adam Yates (Orica-Bike Exchange) before the standings were updated and Froome was handed the yellow jersey on the podium.
Froome said: “I’m very happy with the commissaires’ decision. I think it was the right thing to do.
“Thanks to the jury and to the organisers.”
Yates said: “I’m happy with the decision.
“I would not want to take the jersey like that. I wanted to take it with my legs.”
Yates now trails Froome by 47 seconds in second place.
Team Sky manager Dave Brailsford said: “It’s a fair decision.”
Froome’s main rival Nairo Quintana (Movistar), of Colombia, is third, 54 seconds behind, with fourth-placed Mollema 56 seconds off the pace.
