It meant it was a bitter-sweet day for Froome who, despite increasing his lead and seeing several top rivals lose time, lost his chief Team Sky lieutenant Thomas and good friend Porte.
Overall, Froome leads Aru by 18 seconds and Romain Bardet by 51 as two-times victor Alberto Contador of Spain cracked on the last climb and dropped out of contention.
A stricken Porte was treated by doctors before being carried into an ambulance and taken to hospital, while Martin picked himself up and finished the stage despite going down for a second time.
With just over 30 kilometres remaining, Chris Froome had a mechanical error and had to change bikes.
He crashed twice while wearing the yellow jersey, on stages two and four, and on Saturday went straight into a hay bale after he and Froome took a corner too fast on a descent during stage eight to Station des Rousses.
Bardet, riding on familiar roads - his AG2R-La Mondiale team is based here - attacked on the final descent and got clear.
Porte missed a left-hand bend, cartwheeled across the road and bowled over another rider, Dan Martin, before slamming into a grassy bank.
Uran, who has never finished higher than 23rd in the Tour, climbed to fourth in the general classification, 51 seconds behind Bardet. Other riders out include LottoNL-Jumbo's Robert Gesink.
One sprinter who will not be there to fight for a second win is Arnaud Demare after the French national champion - plagued by illness - was eliminated with three of his FDJ team-mates for finishing outside the time limit. The Sunweb sprinter was part of the Sunday's large break and battled back after the HC duo of the Col de la Biche and Grand Colombier to win the intermediate sprint and move within 52 points of the Quick-Step Floors rider.