Barak Itzhaki's first-half strike proved enough for Israel to record their first points of the 2004/06 UEFA European Under-21 Championship qualifying campaign.
Having been edged out 1-0 by France in Paris on Friday, Guy Levy's side were keen to bounce back in Tel-Aviv and Beitar Jerusalem FC's Itzhaki scored what proved to be the only goal of the night in the 32nd minute, collecting Gal Alberman's pass and seeing his ensuing shot deflected off Charlambous Charlambous past goalkeeper Demetris Stylianou.
Israel are also at home in their next match, against Group 4 leaders Switzerland on 8 October, while Cyprus face a home game against France four days later.
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