The Lotto-Soudal rider clinched his third stage win on the Tour this year ahead of his compatriot John Degenkolb (Giant-Alpecin), with Norwegian Alexander Kristoff (Katusha) taking third place at the end of a hilly 183km ride from Mende.
Greipel launched his sprint with about 200 metres left and held off Degenkolb to bag his ninth stage win on the Tour.
Briton Chris Froome retained the overall leader's yellow jersey after staying safe in the bunch all day in an unchanged top 10 in the general classification.
The Team Sky rider leads Colombian Nairo Quintana of Movistar by 3:10 with American Tejay van Garderen (BMC Racing) in third place, 3:32 off the pace.
Froome, who had urine thrown at him by a spectator on Saturday, praised the 'fantastic atmosphere' during the stage.
"None of that silly stuff happened today," said Froome.
"Thousands and thousands of people are the heart and soul of this race. As I said (those people responsible for the incidents) are a minority of people. Today was great, the support on the road was fantastic."
Looking to add to his 26 Tour de France stage wins, Briton Mark Cavendish never contemplated victory, being dropped early on with numerous other riders including last year's runner-up Jean-Christophe Peraud, who crashed heavily on Friday.
The group crossed the line more than 15 minutes behind Greipel.
Slovakian Peter Sagan kept his grip on the green jersey for the points classifications after finishing fourth, having also collected points in the intermediate sprint.
Tinkoff-Saxo rider Sagan, who finished second in four occasions in this Tour, has 360 points to Greipel's 316.
"I think the green jersey is gone, Peter is too strong, he's in the breakaways. He deserves it," said Greipel.
Sagan featured in the day's breakaway that built a three-minute lead over the pack but the sprinters' teams controlled the gap and reined them in, Lotto-Soudal setting him up perfectly for the sprint.
Italian Matteo Trentin tried his luck solo with a brutal acceleration 3.3 km from the line but he was caught with 1.2 km left.
Monday's 16th stage is a 201-km trek from Bourg de Peage to Gap featuring two second category climbs and a tricky descent to the finish.
(Reporting by Julien Pretot; Editing by Ed Osmond and Pritha Sarkar/Gene Cherry)
Share
