After five games, Switzerland have a two-point advantage over Albania and Iceland, who both won on Friday, and while they will remain confident of earning a place in next year's finals in Brazil the Swiss may yet regret their missed opportunities.
Cypriots, worried by the national banking crisis engulfing the country, stayed away from the GSP stadium in their droves and failed to see their team bank a rare World Cup point, which at least took them off the bottom of the table.
Switzerland enjoyed most possession and had more chances but Cyprus could have punished them on several counter-attacks.
The best of those came when Dimitris Christofi's fine shot was tipped wide by diving keeper Yann Sommer in the 56th minute.
Switzerland's influential Bayern Munich winger Xherdan Shaqiri went close seven minutes later, cutting in from the right and driving a low left-foot shot just wide.
Shaqiri created more danger in the 79th with a shot into the box that was deflected out to Valentin Stocker but he could only find the side netting.
With Michel Pont's Swiss team pushing hard for a late winner, they left gaps at the back and Cyprus's substitute midfielder Giorgos Efrem exploited that space with a great through ball to Christofi but his attempted chip was off target.
Switzerland grew increasingly desperate and went close twice in the final minutes when Haris Seferovic forced a save from Antonis Georgallides and then substitute Erin Derdiyok later screwed a shot wide from a promising position.
Cyprus have four points from five games and are one spot and one point above bottom team Slovenia.