Viviani, riding for Quick-Step Floors, finished the 167-kilometer (104-mile) leg down the Mediterranean coast from Haifa to Tel Aviv in less than four hours before thousands of chanting fans.
But the experienced Italian kept his cool and leant his shoulder into Bennett, who veered back to the left, leaving a channel for Viviani to burst through and win. Viviani, 29, wasn't best pleased with Bennett but his victory proved ample compensation.
"As everyone saw, he changed direction".
"This is all I wished, the win and quite a lot of time on the other GC riders", Dumoulin said.
Italy's Enrico Barbin (Bardiani-CSF) consolidated his lead in the blue jersey king of the mountains classification while Viviani's team-mate Max Schachmann retained his white jersey in the youth standings.
Having been surprised by the lush green vegetation at the side of the road on Friday and Saturday, Viviani now got what he was expecting. "It was chaotic because of all those corners and roundabouts, but we can be proud of ourselves", Viviani said. "We did around 2,000 metres of up and down and at some point the group was really stressful about the wind".
After a boring stage through the desert, the final 5km saw the touch paper lit with a brutally fast pace set by Quick-Step Floors into the sprint finish.
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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. "We knew that the second sprint was the one with bonus time and we thought that if it was within grasp, and the breakaway wasn't too far away, we would try".
But he admitted he was anxious during the break-neck run in to the finish where the peloton was strung out around several roundabouts.
"I was really nervous this morning, I tried to overcome a bit this emotion but it's not easy".
"It was maximum effort to move up as much as possible through the roundabouts". I have already taken part in all three Grand Tours and I consider the Giro as the most hard to finish.
"I think Viviani, he sprinted but he didn't go full", admitted Dennis.
From Eilat, the riders and their staffs will fly to Catania, Sicily, from where they will climb the Italian boot to Cervinia on the border with Switzerland.
It won't be as straightforward when the race resumes on Tuesday night after a rest day, with a hilly stage ending in an steep uphill finish on the agenda - providing Bennett and his rivals with their first chance to strike a blow on Italian soil.