The Dutchman needed no help from his team mates in the final straight as he slalomed through his rivals to beat German Andre Greipel by nearly a bike length after 181 kms from Dreux, with Colombian Fernando Gaviria crossing the line third.
Groenewegen said: "My legs are better every day".
Gaviria and green jersey holder Sagan, who have won two stages each in this year's race, ended up following Groenewegen home in a line without ever looking likely to challenge him, with Arnaud Demare in fourth.
North Koreans Miss Meeting About US Soldier Remains
The US military has since announced that 100 wooden coffins have been moved to the inter-Korean border in preparation. What about the planned repatriation meeting? It had been expected at the inter-Korean truce village of Panmunjom.
Five years after his first stage win and the last Irish victory on the Tour, at Bagneres-du-Bigorres in the Pyrenees, Martin took glory on the shorter but equally steep slopes of the aptly named Mur de Bretagne, or "Wall of Brittany". "I saw Gaviria and Greipel were fighting for position but I saw the finish line and thought, 'This is the moment". All the GC contenders finished in the main pack.
"Having already lost 53 seconds on the stage - finishing 46th after a big effort from team-mate Soren Kragh Andersen, in the white jersey, to minimise their losses, he now drops to 19th - 1'23" behind yellow jersey Greg van Avermaet.
Four-time victor Chris Froome remained over a minute behind Van Avermaet, a support rider for BMC leading hope Richie Porte.
Nishikori predicts 'war' with Djokovic in quarters
It will be Djokovic's first Grand Slam semi-final since the 2016 US Open as he continues his bid to return to the top of the game. Next up for the Spaniard is a blockbuster last four showdown with Serb Novak Djokovic .
The mostly flat 181-kilometer (112-mile) ride from Dreux to Amiens was won by Groenewegen in 4 hours, 23 minutes.
The mostly flat 181-kilometre (112-mile) ride from Dreux to Amiens comes before the three-week race faces one of its most hard legs when it hits the tricky and occasionally treacherous cobblestones. "I've had so many second places at the Tour since the last one".
Fans helped celebrate Bastille Day by waving French flags along the side of road as the riders moved north of Paris through wheat fields to Amiens, the birthplace of French President Emmanuel Macron. The result was another mostly calm ride. I didn't think it was going to happen, but the legs just were there.
Deux changements face à l'Angleterre — Belgique
Je suis très fier pour les gars, pour le pays, simplement heureux de jouer pour cette équipe. La finale du mondial France-Croatie est programmée dimanche (17h00 françaises).
Martin and 11 other riders couldn't reconnect and Martin lost more than a minute, falling from 21st to 31st place at 2:47 behind.