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.
"It's fantastic. I don't know what to say", Fuglsang said.
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BMC rider Porte attacked in the finale featuring a small part of the iconic Alpe d'Huez ascent to gain eight seconds on two-time Tour de France victor Alberto Contador (Trek-Segafredo) and 24 on defending Tour champion Chris Froome. There's still a long way to the Tour but I'm really happy with my condition now.
Fuglsang's move saw him leapfrog race leader Porte and win the race overall, with the Australian finishing second, ten seconds back.
It looked like being enough despite the gradients on the final stage but Fuglsang threw a spanner in the works, cementing his place as a contender for the Tour de France. "Even with the jersey I can't believe it, I've been close to the yellow jersey many times in my career".
Froome's latest defeat means that for the first time since 2013, the 32-year-old old will start the Tour de France with no prior victories in the season.