The 29-year-old defending champion established a two-minute lead over his Silence-Lotto rival when he powered ahead in the company of Polish rider Sylvester Szmyd, of the Liquigas team.
The Pole took the stage win, accelerating first over the line at the summit of the 1,909-metre high mountain having apparently tricked Valverde into thinking he had slowed down.
Valverde planned his breakaway as the riders tackled the climb concluding the 154 kilometre stage from Valence.
The Spaniard, who dons the yellow jersey of race leader, has now established a 16-second lead over Evans in the overall race standings.
"I was happy with the time trial I did yesterday and even though I was not at my best, I felt okay," said Valverde.
"So today I felt I really had the legs to attack 10 kilometres from the finish and put everything into it," he added.
Evans said: "It was a bizarre race. It seemed not many riders want to win the Dauphine.
"It's hard to have the responsibility of wearing the yellow jersey as well as coping with the wind on the final stretch, that's tough on the Ventoux. I was expecting Contador to do more."
Although Szmyd came second in the same setting here two years ago, it was the first ever stage win in a major race for the 31-year-old from Warsaw.
On Friday the riders face a 106-kilometre stage from Gap to Briancon. The race, a key build-up event for next month's Tour de France, concludes in the Alpine city of Grenoble on Sunday.
Source: AFP Global Edition