Nizzolo (Trek-Segafredo), one of the favourites to win the largely sprint-friendly stage, edged Germany's Nikas Arndt (Giant-Alpecin) into third place.
Dutchman Steven Kruijswijk (Lotto NL-Jumbo) finished in the main pack and kept hold of the pink jersey while maintaining a three-minute advantage over his nearest challenger, Colombia's Esteban Chaves (Orica-GreenEDGE), with four days left.
Kluge is the third German to win a stage at this year's Giro, after Andre Greipel and Marcel Kittel, although his team IAM Cycling announced on Monday that they would close down after this season as they had failed to find a co-sponsor.
(This version of the story corrects name from Klose to Kluge in final paragraph)
(Reporting by Simon Jennings in Bengaluru; editing by Ken Ferris)
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