Johann Gudmundsson scored a hat-trick as Iceland grabbed an unlikely point despite trailing 4-1 early in the second half.
The visitors had taken an early lead but appeared to be out of the match when Switzerland, 1-0 winners over 2014 World Cup hosts Brazil in a friendly last month, scored three goals in a 15-minute spell.
Despite the embarrassment, Switzerland, aiming to qualify for their third successive World Cup, have a four-point lead at the top of European Group E with three matches to play.
Iceland stunned the crowd at the Stade de Suisse in the third minute when Gylfi Sigurdsson crossed from the left and Gudmundsson was given time to bring the ball under control and fire it into the roof of the net with a shot on the turn.
Stefan Lichtsteiner levelled the score in the 15th minute when he headed in Granit Xhaka's outswinging cross and central defender Fabian Schaer put them ahead in the 27th, snapping up a rebound after Hans Seferovic's shot was parried by Hannes Halldorsson.
Three minutes later, Xherdan Shaqiri burst from the halfway line and slipped the ball to Lichtsteiner, who drilled in a low shot from the edge of the area
Dzemaili extended the Swiss lead when he blasted in a penalty in the 54th minute and the hosts appeared to be home and dry.
Instead, Kolbeinn Sigthorsson powered through the Swiss defence to pull one back for Iceland two minutes later.
Gudmundsson reduced the arrears further in the 68th minute and Iceland, who have never played at the World Cup, completed a remarkable fightback when the Dutch-based forward curled in a brilliant shot from the edge of the area in stoppage time.
Unbeaten Switzerland have 15 points from seven games and visit Norway, who have 11, on Tuesday. Iceland have 10 points.
- Sports & Recreation