Nir Biton added the second with a glancing header in the 22nd and Tomer Hemed with a penalty (26) plus a goal by striker Munas Dabbur (38) after a slalom run wrapped up the win.
Israel are in third place, which brings a playoff spot, on 12 points from seven games behind group leaders Wales, who have 17 after beating Cyprus 1-0 away, and Belgium with 14 after their 3-1 home win over Bosnia.
Cyprus have nine points and Bosnia eight with Andorra bottom without a goal or a point.
Israel laid siege to the Andorra goal for the entire second half but failed to add to the score.
Their next fixture is away to group leaders Wales, who won 1-0 in Cyprus, on Sunday where a win for the hosts will ensure they qualify for the finals.
"I feel confident in my players and the serious approach of the team but we know that against Wales it will be totally different," Israel coach Eli Guttman said.
"They will want to celebrate their qualification with a win ... but if we want to ensure a third-place finish in the group, a result against Wales will be very important."
(Writing by Ori Lewis; Editing by Ken Ferris)
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