It was Viviani's second consecutive stage victory after he also won the race's second stage from Haifa to Tel Aviv on Saturday.
Viviani overcame route "beer Sheva - Eilat" in 5 hours 2 minutes 9 seconds.
"And as I understood that you really have to make the most of your time off, it was really important for me having Elena, who's a cyclist and understands these situations".
Viviani edged fellow Italian Sacha Modolo of EF Education First-Drapac p/b Cannondale at the finish line and pumped his fist in triumph in a near repeat of his sprint victory in Tel Aviv on Saturday.
The 120 million shekel (34 million dollars, 27 million euros) investment in the Israeli leg attracted thousands of tourists as spectators watched to see whether four-time Tour de France champion Chris Froome, victor of three Grand Tour titles in a row.
The fourth stage will be held in Sicily (Catania - Calagione, 198 km).
"But I felt better later on".
Italian Jakub Mareczko was second with Bennet taking third.
Australian Dennis (BMC) made up for his disappointment in losing Friday's opening time trial by two slender seconds to Team Sunweb's Dumoulin by winning the second intermediate sprint and moving one second clear of the Dutchman in the general classification.
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"The team rode for me in the 30km before the intermediate sprint and delivered me perfectly", said Dennis, who beat Viviani in that race within the race.
I don't know if it was the shock of racing again after five weeks but whatever the reason as Ed Sheeran might say, my legs didn't work like they used to before. He is now 19th, 38 seconds behind the leader.
The riders will leave Israel for Italy on Monday, with the Giro to resume on the island of Sicily on Tuesday. From Cervinia, the Giro will move on May 27th to Rome for the 21 and last stage.
The Giro d'Italia's Israeli excursion is over, and now the excitement begins.
While there were fewer spectators on 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.
Deemed as the world's second most prestigious cycling competition after the Tour de France, it was arguably the biggest sporting event ever to be held in Israel.
He praised the enthusiasm of the Israeli fans he encountered over the three days.