Holders Italy made a humiliating exit in the World Cup group stage after losing 3-2 to Slovakia on Thursday, having been largely outplayed.
Slovakia's win put them through to the second round as Group F runners-up to Paraguay, who drew 0-0 with New Zealand.
Italy finished bottom of the section with just two points.
Slovakia striker Robert Vittek scored after 25 and 73 minutes and Kamil Kopunek added a third in the 89th for the World Cup debutants at a stunned Ellis Park, where Italian flags stopped waving almost from the start.
Antonio Di Natale and Fabio Quagliarella scored late on for Italy but the group favourites were always chasing the game.
"Everybody had the desire, the dream to get through but we didn't and it's our fault," said Italy's injured first-choice goalkeeper Gianluigi Buffon. "If you can't win it is right to go home. We will have to look at what happened".
Slovakia goalscorer Vittek told a news conference: "It's a huge success. We've moved the limits of Slovak football. We couldn't have dreamt about this."
"Of course, we didn't expect such domination. We were better during the match. We played with our hearts and that's what decided the match today," he added.
Slovakia, who made four changes to boost their attacking options given they had to win to have any hope of qualification, started brightly and showed a speed of movement which Italy have severely lacked all tournament.
The Azzurri drew 1-1 with Paraguay and New Zealand in earlier lacklustre displays and more sloppiness led to Slovakia's opener.
Daniele De Rossi gave the ball away and Slovakia attacked straight at the heart of Italy's wide open defence. Juraj Kucka played the ball through for a falling Vittek to score from the edge of the box beyond the reach of keeper Federico Marchetti.
Vittek netted his second at the near post from close range and, after Di Natale pulled one back for Italy after 81 minutes, substitute Kopunek grabbed a third for Slovakia.
Quagliarella made it 3-2 with a delightful long-range chip over Jan Mucha but it was too late for the Italians.
With France also going out at the group stage, it is the first time the two finalists from the previous tournament have failed to make the knockout round.
The amazing defeat brought an abrupt end to Marcello Lippi's time as Italy coach and the international careers of Fabio Cannavaro and Gennaro Gattuso after the trio said this would be their last tournament with the national side.
Italy's best chance in the first half came when Slovakia's Martin Skrtel headed narrowly over his own bar, a mark of how poor Italy have been in South Africa, while Skrtel cleared Quagliarella's shot off the line in the second period.