Fuglsang (Astana) finished ahead of Dan Martin (Quick-Step Floors) and Louis Meintjes (UAE Team Emirates) to take the short, sharp and mountainous 115km stage from Albertville to Plateau de Solaison.
“It's amazing. I don't know what to say,” Fuglsang said. “Even with the jersey I can't believe it, I've been close to the yellow jersey many times in my career.
“We tried to keep our positions on GC and it came down to a big big fight for the overall victory. We planned it very well with Fabio [Astana team-mate Aru] attacking with Alejandro Valverde in the Col de la Colombière and everything went in our favour.
“We played really smart. Froome had to pull after Fabio and Valverde. I tried to keep cool all day, and without pushing too much I went for the stage win and I got it all.”
A group of 24 riders went clear at inside the first 20km of racing but it was Tony Gallopin (Lotto Soudal) who crested the Col des Saisies alone with an advantage of 50 seconds over Porte.
Gallopin’s efforts soon ended when the race exploded with Chris Froome (Sky) attempted to put Porte under increasing pressure.
Alejandro Valverde (Movistar) and Fabio Aru (Astana) did the same when they rode away from the remains of the peloton and crested the Col de la Colombière with an advantage of a bit more than one minute
Behind, Froome continued to put more distance between him and Porte in the downhill before he and a significant 10-man group containing Fuglsang, Martin and Meintjes gathered up Valverde and Aru with 10km to the final climb.
Martin attacked with 7km to go but Fuglsang bridged quickly and went solo 5km before the end as Porte regrouped to pass and drop the majority of the riders who were previously ahead of him, including a spent Froome, Valverde and Alberto Contador (Trek-Segafredo).
Once it was established Fuglsang would win the stage and the 10 bonus seconds on offer, the race came down to a race against the clock for Porte on the Plateau de Solaison.
However, the Australian's efforts fell just short even as he demonstrated the grit required of a Tour de France favourite.