Porte latched onto Alberto Contador's eventually unsuccessful bid for the overall win, joining the Spaniard in an attack on the final climb with Lotto Soudal's Tim Wellens that saw the trio finish just ahead of the yellow jersey group of race leader Geraint Thomas (Team Sky).
Porte's third-place finish on the day was enough to lift him into third in the overall standings past Katusha's stage 6 winner Ilnur Zakarin.
"It was an incredible day," Porte said. "When Contador attacked at the bottom of Côte de Peille it was a long way out and then Team Sky obviously chased back. I've got to pay credit to my teammates who put me where I needed to be and put me in the best position at the bottom of Col D'Èze."
Porte said the race came down to who had the strongest legs in the thrilling finale.
Porte added that the podium result, after winning here last year while targeting the Giro d'Italia in May, gives him confidence going into the next part of his season.
It is Porte's second WorldTour podium result this season having finished second overall at the Tour Down Under in January.
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BMC Racing director Fabio Baldato acknowledged that Porte and the team appear to be on the right track heading into the heart of the season.
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