Porte, the 2013 Paris-Nice champion, was over 11 minutes in arrears when Froome came over the finish line alongside rivals Alejandro Valverde, Alberto Contador and Cadel Evans among others.
It meant Valverde, whose Movistar team were protagonists on most of the day's five categorised mountain climbs, has moved up to second place, only 1m 25s behind Froome.
Bauke Mollema (Belkin) moved up to third overall ahead of fellow-Dutchman and teammate Laurens Ten Dam, while Spain's two-time winner Contador moved up one place to sixth at 1:51 off the pace.
Martin's maiden win on the race, a few months after he lifted his biggest race at Liege-Bastogne-Liege, put the Irishman into the top 10 where he is eighth overall at 2:28.
He is from solid cycling stock, being the nephew of former Tour de France, Giro d'Italia and world champion Stephen Roche.
Martin had hoped to slip into an early breakaway and go on to fight for the win but during an epic day of racing, the Irishman was forced to attack Froome's group of favourites on the final climb.
He and Fuglsang crested the summit with a 40sec lead on the chasing peloton and held them off on the 30km descent into Bagneres.
"I was confident in the final, I knew I could produce the speed I needed but after such a hard stage, but you're never sure," said Martin.
"To come across the line and realise I've won a stage of the Tour de France was amazing . . . but I was so focused on his (Fuglsang's) wheel, and on the finish line and getting their first."
