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.
"We went up Col D'Èze so fast but then we also came down at warp speed," he said. "We could see that they were coming back at us but it was just a great way to finish off a solid week of racing."
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.
"My goals this year have changed and now my big aim is the Tour de France in July," he said. "After coming back to Europe two weeks ago and not really knowing where I was at, finishing third in such a hard Paris-Nice is a good sign for the future."
It is Porte's second WorldTour podium result this season having finished second overall at the Tour Down Under in January.
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.
"Paris-Nice has been the first real test of the season for these guys and our goal was to be on the podium," he said. "To have Richie up there today shows that he is in good form and that the team worked really hard to support him all week.
"It wasn't an easy week of racing," Baldato said. "There were a lot of good GC contenders and the extreme conditions that the peloton faced didn't make it any easier. We're walking away happy with our performance."
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