The Italians took a two-goal lead with just over half an hour gone when Graziano Pele slotted home in the 14th minute and Antonio Candreva converted a penalty in the 31st.
Israel got themselves back into the match in the 35th when forward Tal Ben Chaim lofted a ball over goalkeeper Gianluigi Buffon, who was caught off his line, and the momentum shifted.
They received a further boost in the 55th when Chiellini was sent off for the first time in his international career after a second booking and the hosts pushed for an equaliser.
But Israel squandered a handful of chances and were dealt a final blow in the 83rd minute when Italy substitute Ciro Immobile powered past the defence and blasted home a low shot from the right of the area to secure all three points.
(Writing by Ori Lewis; editing by Ken Ferris)
