The hosts rarely threatened despite the 42nd-minute dismissal of Loukas Vintra after the Greece defender picked up two yellow cards, but the visitors ran out of steam in the closing stages as strikes from Stephane Grichting and Marko Padalino sealed three points for the Swiss. The win moves Switzerland top of the group with 16 points, while Greece are second with 13 points ahead of Wednesday's clash with Moldova in Chinsnau.
Greece began in lively fashion and could have gone ahead after just one minute when Ioannis Amanatidis found space in the box but his limp shot did not trouble the Swiss goalkeeper Diego Benaglio. Amanatidis came close again in the 25th minute but his curling shot form inside the area sailed over the bar.
Visiting goalkeeper Kostas Chalkias was rarely troubled in the opening half, with the hosts not having their first serious chance until the 41st minute when Tranquillo Barnetta slalomed down the left before his powerful shot was deflected wide. A minute later, Greece were reduced to 10 players when Vintra was sent off after collecting his second yellow card.
The Greeks were unfazed by the numerical disadvantage and continued to play with confidence, enjoying their best chance after 67 minutes when Amanatidis played in overlapping full-back Nikos Spiropoulos, whose powerful shot was tipped on to the crossbar by goalkeeper Diego Benaglio. The breakthrough finally came for the home side seven minutes from time when Grichting headed home Hakan Yakin's free-kick from the right flank.
The home crowd were celebrating again four minutes later when Padalino scored with another header, powering home Alexander Frei's chipped left-wing cross.