German Tony Martin (Etixx-Quick Step) retained the overall leader's yellow jersey.
Lotto Soudal rider Greipel, who holds the green jersey for the points classification, started his effort late in the final straight but easily went past Britain's Mark Cavendish (Etixx-Quick Step).
Cavendish, looking far from his past best as he sought to add to his 25 Tour stage wins, again came up short and finished third after taking fourth in Sunday's second stage won by Greipel.
Slovakian Peter Sagan (Tinkoff-Saxo) finished a strong second at the end of a 189.5-km ride marred by seven crashes on the slippery roads of northern France.
"Two victories, it's great," said Greipel.
"The whole team worked well for this sprint. It was the first bunch sprint, it's interesting... with 300 metres I thought I was boxed in but I saw an opening and went for it."
France's Nacer Bouhanni was an early casualty of the pile-ups, abandoning the race when he was caught up in a crash that involved four of his team mates.
The sprint ace, who was looking to win a stage and possibly aiming for the green jersey, was taken to a hospital for checks.
His Cofidis team manager said the 24-year-old had not suffered any fracture.
WIth 77 km left, the BMC and Sky teams at the front accelerated and split the peloton as crosswinds made for yet another nervous day on the Tour. No big guns were trapped behind and the favourites avoided trouble.
Martin still leads Briton Chris Froome (Sky) by 12 seconds overall and American Tejay van Garderen (BMC Racing) by 25.
Spain's Alberto Contador (Tinkoff Saxo) remains eighth, 48 seconds behind, while defending champion Vincenzo Nibali (Astana) is 13th and 1:50 adrift. Colombian Nairo Quintana (Movistar) lies 17th, 2:08 off the pace.
Greipel leads the points classification with 151 points, 32 ahead of Sagan.
The ride took the peloton through several World War I battlefields on a day of remembrance on the Tour.
Early in the morning, a metal blue cornflower was inaugurated at Mont St Eloi, where 1909 Tour winner Francois Faber died 100 years ago.
(Reporting by Julien Pretot, editing by Alan Baldwin)
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