The race will then transfer to Italy, and the island of Sicily, for an early rest day on Monday.
Dumoulin was the last of the 175 riders to start the stage and finished the 9.7-kilometer (6-mile) time trial in 12 minutes, 2 seconds to claim the pink jersey.
Sacha Modolo (Cannondale-Drapac) finished second as Bennett faded into third on the 229km stage from Be'er Sheva to Eilat, the longest of this year's race.
Viviani was again the strongest among the sprinters, but this time the victory was given to the Italian challenge.
Elia Viviani said he wouldn't have been able to win Saturday's Giro d'Italia stage in Tel Aviv had he still been riding for British team Sky.
After two days of unseasonably hot temperatures, the heat wave that blanketed the country over the past few days finally broke Saturday night, although temperatures still reached around 35°C (around 95°F) in the desert on Sunday. Tom Dumoulin behind him for a second.More news: Appeal com'tte begins sitting Monday — APC Ward Congresses
Thousands of cyclist fans lined the route on Saturday, as competitors sped through the historic cities of Acre and Caesarea, ending the race in Tel Aviv's Charles Clore Park close to the Port town of Jaffa.
Since 2006, the Giro has commenced alternate years with a "Big-Start" competition outside of Italy.
At one point on the only categorised climb of the day, a clutch of fans swamped the two breakaway riders battling for mountains points and from the overhead helicopter camera it was hard to make out the riders amongst the bodies in the road.
This race has exceeded my expectations. "Israelis are the greatest fans in the world", he added.
Jerusalem's opening leg was named in honor of Gino Bartali, a three-time former Giro champion who in 2013 was posthumously named a Righteous Among the Nations, Israel's highest honor given to non-Jews who risked their lives to save Jews during the Holocaust.
The Giro has been warmly embraced in Israel. The riders were cheered along the 226km route by groups of local supporters, with many having prepared visual displays on the roadside in pink, continuing the Israeli public's enthusiastic embrace of the Giro d'italia. "This was a Giro d'Israel, a three-day tour around our special country". In contrast, the Super Bowl had 114 million viewers.
"For me, Israel has already won this race, as it afforded hundreds of millions of TV spectators to see our handsome country and feel the warmth of our people", he told The Associated Press.