Irish rider Martin broke with one kilometer remaining on the final climb with French rider Pierre Latour offering the only competition. Alejandro Valverde of Team Movistar finished in 3rd. Martin's timing was perfectly judged and he was able to hold onto until he crossed the line.
"I was a bit nervous because of the headwind, I didn't think it was going to happen," Martin, 31, said. "I thought, why not have a try? So I did.
"Today I just attacked as hard as I could. It makes this Tour de France a success for us already, and anything else is a bonus."
Greg Van Avermaet retains the yellow jersey and remains first in the general classification for the fourth consecutive stage.
Tom Dumoulin, winner of the 2017 Giro D'Italia, suffered badly following a mechanical issue with only 5km to go, dropping 40 seconds on the leaders.
Courtesy of ESPN