On the second day back in Italy following three opening stages in Holland, Lotto sprinter Greipel had been looking to redress the balance after seeing compatriot and sprint rival Marcel Kittel (Etixx) claim two consecutive stage wins.
But after a ferocious sprint to the finish of the 233km stage from Praia a Mare in Calabria, Greipel, known as the 'Gorilla' for his impressive physique, followed his victory roar by crumbling on the roadside as he tried to recover from his efforts.
Arnaud Demare, the French winner of Milan-SanRemo in March, finished a distant second for FDJ with Italian Sonny Colbrelli claiming third place for Bardiani.
Dumoulin, who races for Giant, took the pink jersey after his time-trial win on the opening stage and reclaimed it on Tuesday when he finished second behind Lampre's Diego Ulissi on stage four.
The Dutchman will wear it going into Thursday's sixth stage, one of several in the medium mountains that should see the sprinters dropping to the back of the pack.