Ottmar Hitzfeld's men pulled two points clear of second-placed Iceland but they would be enjoying a four-point cushion had Haris Seferovic scored in second half stoppage time. Cyprus, meanwhile, move off the bottom and above Slovenia thanks to a point earned from an impressive display in which Dimitris Christofi twice went dangerously close.
Gokhan Inler warmed Antonis Georgallides' palms first but it was Cyprus who would dominate the early exchanges. Compact football allowed Christos Theophilou in for a free header before Konstantinos Charalambidis blasted just past a post.
Sommer on song
Xherdan Shaqiri then spurned a clear chance and the Swiss were nearly punished when Yann Sommer was forced to tip Christofi's drive to safety. Konstantinos Makridis came even closer when he hit the upright in the 33rd minute.
Cyprus pressed on after the break and Sommer did well to push another Christofi thunderbolt over his crossbar. Shaqiri then repeated the trick at the other end with Georgallides equally wise to the move.
Both sides enjoyed late chances to score a winner, with Georgios Efrem's dipping drive being held by Sommer three minutes from time. Then, seven minutes into time added on, Seferovic nodded the ball just off target from six yards out.