The Swiss, who reached the finals for the second time in a row, had most of the possession but their inaccurate finishing combined with good defending saw them hanging on nervously for the point they needed.
The hosts were also missing three key players who went down with a virus this week, goalkeeper Diego Benaglio, midfielder Benjamin Huggel and record scorer Alex Frei.
"Frei was very disappointed and I can understand that," said coach Ottmar Hitzfeld. "But I'm the coach and have the responsibility. There was a World Cup qualification at stake.
"We played a good game today," said forward Eren Derdiyoi. "We wanted to keep a clean sheet without fail, and we have achieved that.
Benaglio added: "It was much more difficult to watch from the stands that on the pitch. The end was nerve-wracking but the team played the final minutes with great concentration.
Israel's few chances came mainly on the counter-attack but they hardly troubled Swiss stand-in goalkeeper Marco Woelfli in the cold conditions in Basel.
