Dennis was no match, however, for Elia Viviani, of Quick-Step Floors, who sealed his second consecutive stage win in the bunch sprint finish.
Speaking seconds after the stage finish, the stage victor Viviani said: In the first two hours of racing I felt very bad.
Bennett lost out and finished third, with EF Education First-Drapac p/b Cannondale's Sacha Modolo (Italy) claiming second place.
The emotional Italian, who won Olympic ominium gold on the track in 2016, spent three years with the dominant outfit of Tour de France champion Chris Froome but said he left to pursue his own ambitions at his home Tour.
The fourth stage will be held in Sicily (Catania - Calagione, 198 km).
"The pressure was off after yesterday's win, but the final straight was good for me", Viviani said.
"I wasn't overly keen to do it but the team said we're doing it and they did an excellent job, they delivered me perfectly", said Dennis.
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Having changed teams in the off-season, Viviani had a busy start to the year with Quick-Step, winning the Dubai Tour in February, taking the points classification at the Abu Dhabi Tour a couple of weeks later and then finishing second to world champion Peter Sagan at Gent-Wevelgem in March.
Elia Viviani came out on top in a feisty sprint finish to win stage three of the Giro d'Italia in Eilat, while BMC's Rohan Dennis kept hold of the race leader's pink jersey.
Mullen is the best of the Irish on the overall general classification in 46th position, 58 seconds off the lead, while Bennett is 64th, 14 seconds behind his compatriot.
"This was a Giro d'Israel, a threeday tour around our special country". From Cervinia, the Giro will move on May 27th to Rome for the 21 and last stage. While there were fewer spectators Sunday due to the sparsely populated southern Negev Desert than the two previous stages, the riders were still cheered on by locals banging drums and strumming guitars.
"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". It was the closing chapter of a historic three days, during which cycling captured the Israeli public's imagination.
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).
Since 2006, the Giro has commenced alternate years with a "Big-Start" competition outside of Italy.