Gary Speed's side moved off the bottom of Group G with their victory, while the Swiss are now four points behind second placed Montenegro with just one qualifier to play next week.
The turning point came when Switzerland's former Tottenham defender Reto Ziegler was shown a straight red card in the 54th minute for a studs-up tackle on Chris Gunter.
A foul on Gunter by Timm Klose six minutes later allowed Arsenal midfielder Ramsey to slot his fifth international goal from the penalty spot.
Tottenham winger Bale then made the win safe as he raced on to a Steve Morison pass to beat Diego Benaglio for his first Wales goal since the sides met in Basle a year ago.
The Swiss thought they had grabbed the opener five minutes into the second half but Eren Derdiyok's effort was ruled out for offside.
Dutch referee Bjorn Kuipers then showed Ziegler a straight red card after the left-back had lunged into an aggressive challenge on Gunter.
Klose's clumsy challenge on Gunter saw Kuipers point to the spot in the 60th minute and Ramsey's low effort could not be kept out by Benaglio.
Wales sealed victory in the 71st minute as Morison passed between two flat-footed defenders to find Bale in space and the winger raced in on goal to shoot left-footed past Benaglio.