Sagan won his first Grand Tour stage for two years on Monday after finishing second five times at the Tour de France last month, but couldn’t match Valverde’s pace up a short and steep climb to the finish of the 209.6km ride from Estepona to Vejer de la Frontera.
Spain’s Dani Moreno finished third.
Esteban Chaves of Colombia retains his overall lead by five seconds from Dutchman Tom Dumoulin with Ireland’s Nicholas Roche a further seven seconds back.
However, Valverde moves into fourth overall and leads Movistar teammate Nairo Quintana and Britain’s Chris Froome by 11 and 15 seconds respectively in the battle among the favourites to win the three-week tour.
Froome is aiming to become just the third man in history to win the Tour de France and the Vuelta in the same year. – Agence France-Presse