Deceuninck-QuickStep's Viviani crossed the line first at the end of the 219km stage from Vinci and looked to have taken victory in the national jersey, but he was later relegated for changing his line and blocking Trek-Segafredo's Matteo Moschetti.
That elevated Team UAE Emirates' Fernando Gaviria to victory with Groupama-FDJ's Arnaud Demare second.
It was a messy end to a stage which, for the first three-quarters, was taken at a relatively easy pace.
After a late crash had split the peloton in two, a chicane in the final kilometre uncoupled the sprint trains and left the leading contenders to battle it out for themselves.
Stage two winner Pascal Ackermann launched his attack first but had gone too soon, with Viviani, Gaviria and Arnaud Demare coming around the Bora-Hansgrohe rider in the final metres.
But Viviani had veered strongly left, forcing Moschetti to sit up and stop his sprint.
The crash with five kilometres left shook up the general classification too with Team Ineos' Tao Geoghegan Hart the big loser.
The Londoner began the day 35 seconds off Primoz Roglic in pink but, having chased back on to the group with a bloodied knee following a crash around 50km out, was held up by the incident and lost 91 seconds.
Lancastrian Simon Yates remains second overall, with the Mitchelton-Scott man 19 seconds behind Team Jumbo-Visma's Roglic.
The chaotic finish came at the end of a long day for the peloton.
With this the second of three stages of more than 200km to start the Giro following the opening time trial, the pace was considerably down and only one rider - Nippo-Vini Fantini-Faizane's Sho Hatsuyama - was moved to go clear of the pack.
The Japanese rider spent 144 lonely kilometres out in front before the peloton, upping the pace as the threat of crosswinds increased, brought him back.
With 75km left other riders might normally have been tempted to go but instead the peloton remained bunched together, nervously tackling the exposed roads.
The pace was up again heading towards the intermediate sprint in Grosseto and it was then that Hart hit the deck.
With the riders having taken it easy for so long early in the day they had plenty of energy to burn late on, contributing to a wild finish.
