Martin took the ninth stage on Sunday after a dramatic day of racing in the Pyrenees saw yellow jersey holder Chris Froome forced to dig deep to defend his race lead.
Martin, of the Garmin team, came over the finish with his arms in triumph after beating Dane Jakob Fuglsang (Astana) in a two-up sprint.
Froome and all the race favourites arrived 19sec later although the Kenyan-born Briton was the sole surviving member of a Sky team over the 168.5km race from Saint-Girons to Bagneres-de-Bigorre.
Post-race speculation on Saturday, when Richie Porte finished the first day in the Pyrenees second overall at only 51sec behind Froome, suggested Sky could aim for a second consecutive 1-2 finish in Paris on July 21.
However, the Australian was the main casualty of a frantic start to the race, and an even more concerted effort to drop him later on, as teams appeared to collude in an attempt to drop him down the standings and boost their own hopes.
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.
Solid cycling stock
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 1min 25sec 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. – AFP