Albania captain Lorik Cana collected a second yellow card and was sent off in 36th minute after committing a handball outside the box.
Switzerland looked for a second goal to secure their win in the second half but Albania goalkeeper Etrit Berisha produced a number of saves.
In the 87th minute Albania came close to an equalizer but forward Shkelzen Gashi wasted a one-on-one chance as his shot was saved by Switzerland goalkeeper Yann Sommer.
Switzerland were forced to work hard by 10-man Albania but managed to hang on for victory thanks to Schar`s early goal.
The match also saw an international clash for one family as Albanian midfielder Taulant Xhaka played against his brother, Swiss midfielder Granit.
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