"My team did a brilliant job all day and I wanted to finish it off", he said.
"A good rider who is strong today will be strong in the final two weeks as well", the 33-year-old Tasmanian added before the 181km stage from Brest to the top of the two kilometre climb got underway.
While no rider has won the Giro-Tour double since 1998, everyone will be wary of what the four-time Tour champion may have up his sleeve.
Martin saw his chance when Richie Porte broke free from the pack first with nobody immediately trying to catch up.
In a tense finish, Marin 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.
While his team once again showed cracks when finishing 15th of 22 squads in the stage three team time trial in Cholet last Monday, Martin's victory yesterday sees him move into 21st place overall, a minute and 27 seconds behind current race leader Greg Van Avermaet of BMC.
"It's great to get a win after so many second places since the last one", Martin beamed afterwards.
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"I came to this team to be the leader and the pressure at the beginning, of being the leader is why I didn't do so well in Spring", said Martin.
"Then I had to chase and that effort was fatal".
"I'm not sure the riders knew how to take advantage of it, the stage really could have been much more interesting", he said of the course some were describing as riddled with traps. "It's never good to lose time", said Bardet, who has finished on the podium in the past two Tours.
Van Avermaet leads Britain's Geraint Thomas (Sky) by three seconds in the overall standings, with American Tejay van Garderen (BMC) and France's Julian Alaphilippe (Quick Step) at five and six seconds respectively. "There are a lot of twists on the Tour and this time luck was not on our side".
Quick-Step Floors took the lead of the pace in the last kilometres to launch Fernando Gaviria, and other riders like Alexander Kristoff (UAE Team Emirates), Peter Sagan (Bora-hansgrohe), and Dylan Groenewegen joined in the final sprint.
A group of around 40 riders including Froome opened up a gap of over a minute, but Martin and the rest hustled back. After the relatively flat first nine days, the race will head south and into the Alps and then the Pyrenees Mountains.
Friday's flat 143.5-miles leg from Fougeres to Chartres is the longest stage of this Tour.