The Swiss, who top European Group Two with 20 points from nine games, need a point at home to Israel on Wednesday to win the group and make sure of their place in South Africa. They could qualify later on Saturday if Greece and Latvia draw.
Senderos, dropped for the September games against Greece and Latvia because of a lack of match practice at Arsenal, opened the scoring with a looping header following a free kick on the right after six minutes.
Two minutes later he headed another, this time from a Tranquillo Barnetta free kick from the left. The third goal was another header from a set play as midfielder Benjamin Huggel scored at the far post following a corner.
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