Despite the highly-fancied Spaniards dominating most of the play, Gelson Fernandes' 52nd-minute, close-range shot gave the unheralded Swiss the lead and ultimately the match.
Spain, one of the World Cup favorites here in South Africa, squandered numerous chances and now face Honduras next Tuesday in a must-win encounter while Switzerland meet fellow winners in their group, Chile.
In Wednesday's early game in Nelspruit, Chile, also known as La Roja, secured a first World Cup win in 48 years by edging Honduras 1-0 through a late first-half goal from striker Jean Beausejour.
The Group H success ended a 13-game winless run spanning four tournaments for the Chilean 'Reds' since defeating Yugoslavia on June 16 ,1962, to finish third as hosts.
Switzerland are the next opponents for a team coached by Marcelo Bielsa, who is desperate to make the second round from a group including title favorites Spain after failing to do so with his native Argentina eight years ago.
"I think we deserved to win - though we should have scored more goals," said Bielsa, who guided Argentina to the 2004 Olympic title.
Bielsa noted the Hondurans had suffered a blow on the eve of the game when striker Julio Cesar de Leon had to pull out of the event through injury.
"That robbed them of some of their effectiveness," he said.
Bielsa added he left out his top striker Humberto Suazo, who has been getting over a leg injury, as "he has not been able to train properly for quite a while" and was not therefore match fit.
Chile striker Alexis Sanchez admitted his side should have put the match to bed with more goals.
"Thank God, Honduras did not come back to level matters but it is true we should have been out of sight," said the Udinese forward.
Alexis Mendoza, deputizing in the Honduran dugout for suspended coach Reinaldo Rueda, admitted the loss "is not a good start - but their goal was somewhat fortuitous.
"Now we have to knuckle down and improve for the coming matches against Spain and Switzerland," Mendoza said.
The South Americans began brightly as they sought a fourth victory in six clashes with the Hondurans and midfielder Matias Fernandez went close off a third-minute free kick.
An Argentina-born star who plays for Portuguese club Sporting Lisbon, he comfortably cleared the Honduran wall with a free kick and the ball landed on the roof of the net after dipping just too late.
Fellow Chilean midfielder Carlos Carmona was cautioned 60 seconds later by Eddy Maillet, the first referee from the Indian Ocean island of Seychelles to handle a World Cup fixture.
Chile were on top territorially and it took Honduras 18 minutes to create an opening close to goal only for 101-cap Carlos Pavon to disappoint with a weak shot that trickled wide.
Midway through the opening half Fernandez became the second Chilean to be cautioned in a lively game which attracted a large, South African public holiday crowd to the northeast city near the Kruger National Park.
The best-known Honduran footballer, Tottenham Hotspur midfielder Wilson Palacios, was next to be shown a yellow card as Maillet ran out of patience following constant offences.
Persistent Chile pressure finally paid off when slick passing outside the penalty area created space for Mauricio Isla on the right flank and his low cross was turned in by Mexico-based Beausejour.
Agence France-Presse