The 33-year-old MTN-Qhubeka rider, winner of the Tour of the Mediterranean in 2014 and a stage of the Tour of Spain in 2012, surprised the favourites in the final push and held on ahead of Movistar's Valverde.
Italy's Davide Formolo of Cannondale was third at six seconds after the 149km run from Andratx to Mirador d'Es Colomer.
Friday's third day will also be mountainous over 165km from Valldemossa to Deia.