GALLERY: The best Tour de France Photos
The Lotto-Belisol rider seized his opportunity to snatch victory at the end of a gruelling 194-kilometre route, with Alexander Kristoff (Katusha), Samuel Dumoulin (AG2R La Mondiale) and Mark Renshaw (Omega Pharma-Quick Step).
Marcel Kittel (Giant-Shimano), winner of three of the opening four stages, could not find the right road position to contest the late dart for the line and was deprived of another success.
Vincenzo Nibali (Astana) remains in the yellow jersey after staying out of trouble in the peloton, while Peter Sagan (Cannondale) continues to top the sprinters' classification despite Thomas Leezer (Belkin Pro Cycling) taking the only intermediate sprint.
It was Luis Mate, one of the four involved in an early breakaway, who took both points on the category four climbs, but his Cofidis team-mate Cyril Lemoine remains in the polka-dot jersey.
Another tough stage saw further crashes and more retirements, but all the main contenders avoided any trouble as the Tour prepares for some big climbs over the coming days.
Jerome Pineau (IAM Cycling), Arnaud Gerard (Bretagne-Seche Environnement) and Leezer joined Mate in moving to the front at the start of the day, and they remained in the lead for the vast majority of the stage.
But that advantage disappeared inside the final 16 kilometres, with a four-minute lead having been slowly chipped away by a patient peloton.
The field handled the high winds and rain well to ensure they were able to make inroads into the leading foursome, though Mate did prove a tougher nut to crack than the rest.
With 12 kilometres remaining the Spaniard could fight it no more and he gave into the pressure of the chasing pack, and the jostling for position began ahead of the sprint for the line.
Greipel opted not to go with Michal Kwiatkowski (Omega Pharma-Quick Step) in the final kilometre and his decision was vindicated as he secured a sixth Tour stage win of his career.