The Saur-Sojasun rider posted a time of 14:25, 26 seconds quicker than Cofidis' Estonian rider Rein Taaramae.
Maxime Bouet from Ag2r-La Mondiale was third, a further six seconds back.
Coppel, the world under-23 bronze medallist against the clock in 2007, usurped Europcar's Pierre Rolland on GC with the victory.
The 25-year-old, who was 14th in last year's Tour de France, started the day 20 seconds behind French compatriot Rolland.
Stephane Poulhies (Saur-Sojasun) won the first sector of the fifth stage in the morning.
Poulhies beat the French sprinter Justin Jules (Veranda Rideau) and Dutchman Bobbie Traksel (Landbouwkrediet) to the line in a stage that was reduced to 70km.
Bad weather meant the Col de la Baraque was taken off the route.