The sprinters finished well behind the gruppetto, which came in 29 minutes behind stage victor Geraint Thomas (Team Sky) at the end of a 108.5km stage to La Rosière that included two hors-categorie climbs in the first 57km.
It was the first stage of this year's Tour to hit the alps, and Greg Van Avermaet extended his lead in the yellow jersey, as Julian Alaphilippe took out the stage.
"Obviously, Froomey is the leader", Thomas said.
"It is an ideal scenario at the moment", Thomas added. The Alpe d'Huez, the most famous climb on the Tour, an ascent of myth and legend, returns to the schedule after a two-year absence. "I'm going to try to chill out and enjoy it", said Thomas.
Sky calmly rode at its own pace and slowly caught a series of breakaway riders before Thomas kicked into action with 6 kilometres remaining. "Sometimes this happens, and this time, I think it's the best decision for me to recover and to recover well".
Thomas, who is from Wales, required slightly less than 3 1/2 hours to complete the 108.5-kilometre (67-mile) route from 1992 Winter Olympics host city Albertville to La Rosiere Espace San Bernardo ski station.
After his Australian BMC teammate Richie Porte crashed out of the Tour on Sunday, Van Avermaet started the second week with no agenda but to stay in yellow as long as he could, and put in a ride to honour the jersey.
It also means neither rider has been able to add to their career tally of Tour stage wins, leaving Cavendish still four behind Eddy Merckx's all-time record of 34.
Alaphilippe increased his lead over Taaramäe in the descent before the final climb of the day, Col de la Colombiere, and with 20 km to go the French rider was 20 seconds in front. THE Tour de France was hit by a risky prankster today - as a BMX rider jumped over the peloton. The effort earned him a few KOM points as the first across the Col du Bluffy.
Sprinting standout Mark Cavendish, meanwhile, finished far behind and missed the time limit, ending his Tour.