Kerzhakov netted once in each half while Alexander Kokorin and substitute Viktor Fayzulin also scored for the Russians at Ramat Gan Stadium.
Israel is still searching for its first win in Group F, which also includes Azerbaijan, Portugal, Luxembourg and Northern Ireland.
Russians retain perfect record (Photo: Oz Muaelm)
The visitors went ahead in the seventh minute when Kerzhakov curled a well struck free kick into the top corner, leaving Israel goalkeeper Dudu Aouate no chance
Kokorin made it 2-0 in the 18th, capitalizing on an Israeli defensive mix up to fire home from 10 meters out.
Russia controlled almost the entire first half and the closest Israel came to scoring was when Bibars Natcho hit a speculative long-range effort high over the crossbar four minutes before the break.
Israel came out with verve in the second half, winning a succession of corners and increasing the pressure on Russia `keeper Igor Akinfeev.
But the hosts were unable to create any meaningful chances, and when Kerzhakov scored his second of the night the game was all but over. He pounced on a cross from the left wing in the 64th.
Fayzulin sealed the victory in the 77th with a classy, close-range volley.