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.
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.