"It feels really good", said Dennis, who leads defending champion Tom Dumoulin - victor of Friday's opening time trial - by one second.
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Dennis was no match, however, for Elia Viviani, of Quick-Step Floors, who sealed his second consecutive stage win in the bunch sprint finish.
Bennett faded in the final fifty metres as Italy's Modolo (EF Education First-Drapac) surged through to take second place in the 229km stage from Be'er Sheva.
Australian Rohan Dennis of BMC Racing Team kept the maglia rosa that he wrestled away from defending champion Tom Dumoulin on Saturday.
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.
Riders will now transfer to Italy tomorrow, following the controversial Big Start in Israel.
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"The pressure was off after yesterday's win". "I'm feeling really good, and hope to finish my 20th Grand Tour on a high and get a good result here".
Barbin attacked at the outset of the second-longest stage of the race, joining forces with Canada's Guillaume Boivin (Israel Cycling Academy) and compatriot Marco Frapporti (Androni-Sidermec) to build up maximum lead of seven-and-a-half minutes over the sluggish pack.
"It sewed the first seeds of thought about changing teams but that wasn't the straw that broke the camel's back, it was at the end of the season and discovering that Froome would be riding the Giro and once again I might be excluded".
"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". From Cervinia, the Giro will move on May 27th to Rome for the 21 and last stage.
He'd also won a stage in the Tour Down Under in January and triumphed at Three Days of De Panne in March.
The Giro d'Italia's Israeli excursion is over, and now the excitement begins.
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. "This was a Giro d'Israel - a three-day tour around our special country".