BMC rider Porte attacked in the finale featuring a small part of the iconic Alpe d'Huez ascent, to gain eight seconds on double Tour de France champion Alberto Contador and 24 on defending Tour champion Chris Froome.
Overall, Porte leads Team Sky's Froome by 1:02 ahead of Sunday's last stage, a punishing mountainous trek ending on the Plateau de Solaison.
Dane Jakob Fuglsang, who finished Saturday's 115-km stage with Porte, is third, 1:15 off the pace.
Froome's team mate Kennaugh was part of the day's breakaway and he dropped compatriot Ben Swift (United Arab Emirates) on the final climb to claim his second stage win in the Dauphine.
"To win at L'Alpe d'Huez is better than being an Olympic champion,” Kennaugh said.
France's Romain Bardet, last year's Tour runner-up, jumped away from the favourites' group on the penultimate climb to the Col de Sarenne and slashed 42 seconds off Porte's lead.
He is now sixth overall, 2:07 behind Porte and eight seconds ahead of Contador.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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