Wales, already out of the running, went ahead with an Aaron Ramsey penalty on the hour before Gareth Bale broke clear to fire the second 11 minutes later.
Switzerland, who barely created a scoring chance, stayed third in Group G with eight points and dropped four behind Montenegro who drew 2-2 at home to England.
The Swiss, who had qualified for their last four major tournaments, host Montenegro on Tuesday in their final match which is now academic.
Wales had the best chance of a scrappy first half when striker Steve Morison escaped Steve von Bergen only to see his shot saved at point-blank range by Diego Benaglio.
The game centered on a 10-minute spell early in the second half which began when Eren Derdiyok headed home for Switzerland from a free-kick, only to see his effort disallowed for offside with his team-mates already celebrating.
Five minutes later, leftback Reto Ziegler was sent off for a wild challenge and, another five minutes after that, Timm Klose tripped Chris Gunter and conceded a penalty.
Arsenal midfielder Ramsey converted, although Benaglio got his hand to the ball.
Switzerland played at the last two European Championships and two World Cups but their chances of extending that run ended after Morison sent Bale clear to score in the 71st minute.
