The Spanish rider from Rabobank took the honours in an uphill power sprint finish in Charmey after a 158km trek from La Neuveville.
Sanchez, sixth on GC overnight, collected 10 bonus seconds as he beat Gianni Meersman (Lotto-Belisol) and Paolo Tiralongo (Astana) to the line.
Ireland's Matthew Brammeier (Omega-Pharma), Gatis Smukulis (Katusha), Leigh Howard (GreenEdge), Tosh Van der Sande (Belisol-Lotto) and Anders Lund (Saxo Bank) formed an early escape and built up a maximum lead of 5:50.
Team Sky started to reduce the deficit as they crossed the cat-two Le Chatelard climb which peaked with 55km remaining before Latvian Smukulis went for a solo bid for victory with 15km remaining.
But he was caught inside the final 5km, which climbed at an average gradient of 2.8%, before three-time Spanish time-trial champion Sanchez found the power to record his third victory of the year.