Brighton striker Tomer Hemed chipped in with a penalty four minutes later before Munas Dabur competed the scoring seven minutes before the break.
With Sunday's game in Cardiff in mind, Israel boss Eli Guttman took off captain Tal Ben Haim and Zahavi in the second half with the points in the bag.
Elsewhere, Wales moved to within one win of qualification after Gareth Bale clinched maximum points in Cyprus. And Belgium came from a goal down to beat Bosnia 3-1.
GROUP B STANDINGS:
1. Wales Pl. 7, Pts. 17
2. Belgium Pl. 7, Pts. 14
3. Israel Pl. 7, Pts. 12
4. Cyprus Pl. 7, Pts. 9
5. Bosnia Pl. 7, Pts. 8
6. Andorra Pl. 7, Pts. 0