Should stand. With AP Photos.
It was Viviani's second consecutive stage victory after he also won the race's second stage from Haifa to Tel Aviv on Saturday.
Australian Rohan Dennis remained leader of the General classification.
Stage 3 will follow a lengthy 229-kilometer (143-mile) route on Sunday from Beersheba in the Negev desert down to Israel's southern tip of Eilat along the Red Sea.
Viviani edged Italian countryman Sacha Modolo at the finish line and pumped his fist in triumph in a near repeat of his sprint victory on Saturday in Tel Aviv. Yesterday proved I can win and so I wanted it again.
"It was good to see him get the stage win after not giving it to me, but he was kind let's be honest!"
Dennis, 27, had edged out Viviani at an intermediate sprint 91km into the stage to claim the three bonus seconds he needed to take the race lead. Israel Cycling Academy rider Guillaume Boivin won the intermediate sprint of Mitzpe Ramon and came in third for the Faran River sprint.
The female cycling fan gave TV viewers a surprise as the peloton, including Britain's Chris Froome, wove its way past her barrier. He is now 19th, 38 seconds behind the leader.
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"This is the first time I have retained the leader's jersey of a Grand Tour", Dennis said.
On Sunday evening, the riders and support teams will fly to Sicily for a rest day on Monday and resume the tour on May 8.
The Giro has been warmly embraced in Israel.
Finishing in the lead group was a trickier task on stage three, with several riders - including Kiwi rider Tom Scully - losing contact in the crosswinds near the end of the stage as the peloton drifted into one long line. Israelis are the greatest fans in the world. "It is not a given when you go to a new country that maybe doesn't have a long tradition that you are welcomed with such a crowd", he said.
"I've been nicely surprised with Israel: when we race outside of Europe, Australia or the United States, it's pretty quiet on the roads".
Honorary President of "Big Start" Israel Sylvan Adams said: "I thought we reached the pinnacle Thursday with the Team Presentations and gala opening party".
"I'm glad I took the decision to take the Giro d'Italia to Israel" race director Mauro Vegni told Tazpit Press Service (TPS). "For me, Israel has already won this race, as it afforded hundreds of millions of TV spectators to see our lovely 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.