Iceland came back from a three-goal deficit to secure a draw in Switzerland thanks to Jóhann Gudmundsson's hat-trick, rounded off by a stunning added-time leveller.
Gudmundsson put the vistors in front after just three minutes, but Ottmar Hitzfeld's side rallied and held a 3-1 lead at half-time after two Stephan Lichtsteiner goals and another from Fabian Schär. Three points seemed a formality for Switzerland after Blerim Dzemaili converted a penalty early in the second half, but Kolbeinn Sigthórsson responded immediately, before Gudmundsson stole the show.
The striker exploited an early lapse in concentration to put Iceland ahead with a smart finish but the Swiss quickly regained their composure to level on 15 minutes when Lichtsteiner headed in a Granit Xhaka cross.
By the half-hour the home fans had forgotten all about the early setback. Schär was quickest to react to Haris Seferović's blocked shot in the 27th minute, before Xherdan Shaqiri expertly laid on Lichtsteiner's second goal of the night.
Few would have bet against a Switzerland win when Dzemaili converted from the spot, but Iceland refused to roll over. Sigthórsson gave the guests a lifeline on 56 minutes, punishing some careless defending, before Gudmundsson's second cut Switzerland's advantage to just one goal.
Gylfi Sigurdsson could have levelled for the tireless Iceland 15 minutes from time, but the Scandinavians would not be denied. In the dying moments, Gudmundsson curled in a sumptuous goal from the edge of the area to earn a deserved share of the spoils.
Switzerland lead Group E by four points from Norway, while Albania and Iceland are both one point further back and meet next week.