"It was an early break but it was my only opportunity for the stage win as I'd never have got it in a sprint", explained Martin.
"Third is okay, if I win what do I get except an extra point or two?"
"It was a good day, no incident, I'm glad I still have the yellow jersey ahead of tomorrow's stage", said Van Avermaet, who leads Briton Geraint Thomas by seven seconds.
He had accelerated from 19 to 30km/h on a 10 per cent gradient and he went for it with a kilometre to go to the finish line.
Belgium's Greg Van Avermaet, of BMC, retained the overall yellow jersey, while Briton Chris Froome, of Sky, the defending champion, is one minute and two seconds off Van Avermaet's overall lead.
"We knew there would be some crosswinds and other teams were interested in trying something", said AG2R-La Mondiale manager Vincent Lavenu, whose leader Romain Bardet lost half a minute following a mechanical in the finale of Thursday's sixth stage.
World champion road racer Sagan said he'd been happy enough to stay on Gaviria's wheel and keep ahead in the green points jersey race.
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We saw it the other night against England , where Modric was still running the game late on and showing little signs of fatigue. That was just extra motivation for us. "The reality is that none of us know if that's as good as it gets", Southgate answered.
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"Yellow jersey wearer Van Avermaet described the climax as 'an awesome finish".
After the race, Martin admitted that he had gone for it a bit early but it was a risk he felt that was worth taking.
In a quiet stage, separate solo breaks from Yoann Offredo and Laurent Pichon - as well as a brief split in the peloton amid high winds - had all come to nothing by the time 23 miles remained, when the latter was caught by the bunch.
The overall favourites should be tested again in the cobblestoned Stage 9 on Sunday to Roubaix, before heading down to the Alps next week.
Friday will see the riders take on the longest stage of the race at 218km when they take off from Fougeres and finish in Chartres.
Groenewegen, who won the final stage on the Champs Elysees past year, crushed the pedals with 200m to go to easily beat Colombian Fernando Gaviria as the riders hauled themselves from Fougeres to Chartres. Colbrelli pushed the Slovakian all the way but, as he did on stage two, finished second best.
Groenewegen grew up in a cycling environment as his grandfather was a bike manufacturer and his boyhood coach was Jean-Paul van Poppel, victor of nine sprint finishes at the Tour de France.