Costa, who won Tuesday's stage with a similar impressive showing, rode a strong race Friday, leading throughout the 127.1-mile route from Bourg-d'Oisans to Le Grand-Bornand. He kept that lead despite a course that included two early uncategorized climbs and two Category 1 climbs in the final third of the race.
He finished in 5 hours, 59 minutes, 1 second, 48 seconds ahead of Andreas Kloden with Jan Bakelants in third nearly another minute back.
Froome was in a group that finished 8 minutes, 40 seconds behind Costa. Also given that time was Alberto Contador, Nairo Alexander Quintana Rojas, Roman Kreuziger and Joaquim Rodriguez Oliver -- the riders nearest Froome in the General Classification.
As a result, Froome kept his 5:11 edge over Contador and is 5:32 up on Quintana. Kreuziger is 5:44 back and Rodriguez Oliver trails Froome by 5:58.
There are two stages left in the 100th Tour de France. There is a 77.7-mile route Saturday from Annecy to Annecy-Semnoz that features a Category 1 climb about midway and an uncategorized climb right at the end.
The Tour concludes Sunday with an 83-mile run from Versailles into Paris.