In a chaotic conclusion to the 167km stage in Israel, Italy's Viviani (Quick-Step Floors) darted onto the wheel of compatriot Jakub Mareczko (Wilier-Triestina) before rounding the pint-sized sprinter to win by a bike length.
"This is all I wished for, the win and a lot of time on other GC riders, so it was a flawless start for me and a ideal start for the team".
Sunday's route was the second-longest leg of the 21-day race.
I felt like throwing up after about 500m and eventually lost a minute and 14 seconds to Dumoulin to finish 116th.
Dennis has now become the third Australian and one of only 22 men to lead all three Grand Tours, the Giro d'Italia, Tour de France and Vuelta a España. The Dutchman remained in second place overall as Jose Goncalves moved into third.
Race favourite Chris Froome finished safely in the peloton after a bunch sprint in the Mediterranean coastal resort of Tel Aviv. He is now 19th, 38 seconds behind the leader.
Tomorrow sees the first rest day of the race to allow the peloton and its accompanying circus to head back to Italy, where racing resumes on Sicily on Tuesday with a 198-kilometre stage from Catania to Caltagirone. The Giro will end in Rome on May 27.
Adams hoped the Giro's start in Israel will help grow the sport of cycling locally as well as show Israel to millions of people around the world.
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The race held it's Big Start on Friday with a 9.7km individual time trial in Jerusalem, before a sprint stage on day two to Tel Aviv. While there were fewer spectators Sunday due to the sparsely populated southern Negev Desert than the two previous stages, the riders were still cheered on by locals banging drums and strumming guitars.
Dennis praised the enthusiasm of Israeli fans he encountered over the three days.
"When you race outside Europe, with the exceptions of America or Australia, it can be very quiet, but here they've really taken to the race".
Having led much of Saturday's stage, Israel Cycling Academy's Guillaume Boivin once again hit the front of the race early on, narrowly missing out on the King of the Mountains blue jersey.
Giro d'Italia is the biggest and most prestigious sporting event staged in Israel and coincides with the Jewish state's 70th anniversary.
"For me, Israel has already won this race, as it afforded hundreds of millions of TV spectators to see our attractive country, and feel the warmth of our people, bearing witness that Israel is a diverse, open, free and safe country".
The three Grand Tours now have a tradition of starting outside their home country every second year.