Greipel put on a late surge to finish the 110-mile stretch from Aix- en-Provence to Montpellier in just less than 4 hours, ahead of Peter Sagan, Marcel Kittel, Mark Cavendish and Juan Jose Lobato Del Valle.
Cavendish, the Stage 5 winner, crashed with about 20 miles to go but Greipel -- who crashed twice during Stage 6 last year -- credited Cavendish with being "there at the finish."
"We are hard people: even when we crash, we are still there to do our job a lot of the time," Greipel said.
Daryl Impey took the yellow jersey from teammate Simon Gerrans, becoming the first South African to take an overall lead in the race.
Stage 7, set for Friday, is a 205-mile ride from Montpellier to Albi.