Martin, of the Garmin-Sharp team, posted his first stage victory of the 2013 Tour and moved up to eighth place overall during the mountainous trek from Saint-Girons to Bagneres-de-Bigorre in the Pyrenees Mountains.
He finished less than a second ahead of Denmark's Jakob Fuglsang in a sprint to the finish.
Briton Chris Froome, meanwhile, retained the yellow jersey with a 14th-place stage showing. The Sky Procycling team captain held a 1 minute, 25 second lead over Spain's Alejandro Valverde heading into Monday's rest day.
Froome came under attack at the start of Stage 9 after Sky teammate Richie Porte got off to a poor start and finished nearly 18 minutes behind Martin, leaving Froome to fend for himself against Valverde's Movistar team.
Valverde logged an 11th-place finish in Stage 9, with teammates Nairo Alexander Quintana Rojas of Colombia and Portugal's Rui Costa claiming 18th and 19th place respectively.
Swim Week Miami Beach 2014 [PHOTOS]