The 'Queen' stage of this year's race scaled five peaks in the 161.6 km from Sion to the ski resort at Thyon.
Briton Yates, who rides for Team UAE, launched his attack 4km from the finish, on the long final climb on high roads hemmed by walls of snow, the peloton's first taste of high Alpine passes this season.
He built a lead of 10 seconds over Frenchman Pinot before the Groupama climber counter-attacked and slashed the lead but could not catch up.
Yates took the yellow leader's jersey from his UAE teammate, the young Spaniard Juan Ayuso, who won the time trial on Friday.
"It's a really good performance from the team," said Yates at the finish.
The race finishes with a 170.8km run from Vufflens-La-Ville to Geneva around the lake on Sunday.