The UAE Team Emirates rider attacked with 1.2 kilometres left of the 181km stage from Brest, which finished with two ascents of the 'Alpe d'Huez of Brittany' separated by a rolling 19km circuit.
The Birmingham-born rider held off a late push from AG2R La Mondiale's Pierre Latour to cross the line alone, just ahead of the pack as the general classification hopefuls scrapped for seconds.
BMC's Greg Van Avermaet hung on to the yellow jersey, with Team Sky's Geraint Thomas moving up to second place, three seconds down.
There was a slight split in the peloton, with Chris Froome losing five seconds to a group which included Van Avermaet, Thomas, Adam Yates of Mitchelton-Scott, and Movistar's Alejandro Valverde, Mikel Landa and Nairo Quintana.
There were greater losses further back, with AG2R La Mondiale's Romain Bardet hit by problems on the short two-kilometre climb and Team Sunweb's Tom Dumoulin also distanced after suffering a mechanical problem with six kilometres left.
The general classification showed Yates listed in 13th place and Froome in 14th, both 62 seconds off yellow, and now one second ahead of Dumoulin who dropped to 15th.
Martin, whose other career Tour stage win came in Bagneres-de-Bigorre in 2013, had finished second on this climb when it featured in the 2015 Tour and timed his attack to perfection, launching off the wheel after the Australian had made his own move and riding clear.
Latour's counter-attack came with 500 metres left, but, though the Frenchman closed, he could not bridge over.
"It's great to get a win after so many second places since the last one," Martin said.
"I was afraid of the crosswinds and maybe it was adrenalin, but the legs were there and it all worked out.
"There were a lot of contenders in that group so I was glad to hang on."
