Greipel attacked some 100 meters from the line and held on to beat Slovakian
The mostly flat stage took the riders over 189.5 kilometers (117.5 miles) from Arras to Amiens in northern France, passing some of the battlefields of World War One.
Riders hoping for a stress-free stage after three days of intense racing were to be disappointed as the rain, which largely stayed away the day before, thundered down and turned the slippery roads of northern France into something of an ice rink.
Greipel clinched his second stage win of the race so far, punching the air in delight before even crossing the line. It was the third win overall in five stages for German riders after Tony Martin's success in Tuesday's fourth stage.
The day's seventh and biggest crash happened at the back of the peloton with 15.5 miles to go.
While not as brutal as Monday's huge crash in stage 3, it was spectacular and took down about 30 riders. Three went off the road to the right, tumbling into crash barriers. Behind them, others fell in a domino effect. Frenchman Thibaut Pinot, third on last year's Tour, was among those to fall in his second crash of the day.
Thankfully, because speeds were not as high as on Monday, most riders were more groggy than hurt as they looked to see where exactly their bike was amid a myriad of spinning pedals and jutting-out handlebars.
Martin, a three-time world time trial champion wearing the leader's yellow jersey for the first time, ended the day with a lead of 12 seconds over 2013 Tour champion