Viviani pipped world champion Peter Sagan to the finish line by riding along the barriers after being lead out by team mates Fabio Sabatini and Michael Morkov at the end of the flat 177km stage from Salamanca to Fermoselle.
It was his 17th victory in 2018 and a 60th win for his Quick-Step Floors team.
Viviani's compatriot Giacomo Nizzolo came third.
Yates retained the red jersey despite sustaining a puncture towards the end of the race, coming 51st in the stage and keeping a one-second lead over home favourite Alejandro Valverde and a 14-second advantage over 2016 winner Nairo Quintana.
Italian rider Simone Petilli had to abandon the race after suffering a serious crash with around 40km to go in the stage.
He was taken into an ambulance on a stretcher with suspected shoulder and face injuries and lost several teeth according to reports in the Spanish media.
Petilli becomes the third rider to abandon the Vuelta and the second inside 24 hours following Dan Martin's withdrawal on Monday. Martin has returned home to be with his wife for the birth of twins.
Wednesday's stage 11 is a 207.8km route from Mombuey to Ribeira Sacra. Luintra.
(This version has been refiled to add 'stage' to headline)
(Reporting by Richard Martin; Editing by Toby Davis)
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