Speaking seconds after the stage finish, the stage victor Viviani said: In the first two hours of racing I felt very bad.
Meanwhile, Australia's Dennis kept out of trouble to retain his race lead and ensure that the maglia rosa will be on his shoulders when the race resumes in Sicily on Tuesday.
New Zealand's general classification hope, George Bennett, did a reasonable job, losing 49 seconds in the time trial, and finishing in the lead bunch in both sprints.
Viviani was well off the pace with less than two kilometres to go but the Italian powered home to win comfortably ahead of Jakub Mareczko (Wilier Triestina-Selle Italia) and Irishman Sam Bennett (Bora-Hansgrohe).
Race favourite Chris Froome finished safely in the peloton after a bunch sprint in the Mediterranean coastal resort.
The fourth stage will be held in Sicily (Catania - Calagione, 198 km).
I felt like throwing up after about 500m and eventually lost a minute and 14 seconds to Dumoulin to finish 116th.
Jerusalem's opening leg was named in honor of Gino Bartali, a three-time former Giro champion who in 2013 was posthumously bestowed Israel's highest honor given to non-Jews who risked their lives to save Jews during World War II. The Giro ends in Rome on May 27. They encountered Israeli flag-waving fans and spectators on horseback wearing Giro pink shirts along the way, and even passed a group of goat herders.
He praised the enthusiasm of the Israeli fans he encountered over the three days.
The peloton seemed relaxed as it departed Be'er Sheva with a trio managing to escape pretty easily consisting of Guillaume Boivin (Israel Cycling Academy), Enrico Barbin (Bardiani-CSF) and Marco Frapporti (Androni-Sidermec).
Dennis said the ride through the desert was not as hot as originally feared and that strong winds were the main obstacle as they went through the barren moonscape after passing by its famous craters.
Many in the country associated with organizing the Big Start Israel gave a sigh of relief as the riders crossed the finish line on Sunday, capping off the most complicated, expensive, and logistically challenging sporting event Israel has ever hosted, according to Sports and Culture Minister Miri Regev.