JOHANNESBURG — Spain found just enough of the beautiful game — and a touch of good luck — to advance to the World Cup semifinals, beating Paraguay 1-0 on Saturday night.

David Villa took the tournament scoring lead with his fifth goal, which banked in off both posts in the 83th minute. The goal finished off a brilliant, three-way passing combination that typifies the way the European champions like to play. It sent Spain into the World Cup’s final four for the first time in 60 years.

Spain faces Germany on Wednesday in Durban — a reprise of its 1-0 victory in the Euro 2008 final.

One night after penalty kicks decided Uruguay’s shootout win over Ghana, they were critical in Spain’s victory.

A somewhat subdued match suddenly became chaotic in a two-minute span of the second half. Gerard Pique pulled down Paraguay’s Oscar Cardozo in the penalty area on a corner kick, earning a yellow card and giving Cardozo a penalty kick.

With the vuvuzelas reaching a crescendo, the striker who ended his team’s shootout win over Japan was denied brilliantly this time by Iker Casillas, who dived left to block Cardozo’s low kick.

Seconds later, Villa broke free behind the defense and was hauled down by Antolin Alcoraz, who drew a yellow card. Xabi Alonso went to the penalty spot and sent a wicked drive into the net.

Again, the stadium rocked, but referee Carlos Batres of Guatemala waved off the goal, saying a Spain player entered the area too soon.

Given a second chance, keeper Justo Villar guessed correctly, diving left to stop the penalty kick. He also knocked the rebound away from Cesc Fabregas before defender Paulo Da Silva made a leg save at the goal line on another shot by Sergio Ramos.

After that wild sequence, it seemed anything was possible.

And for Spain, anything is possible with Villa on the field. Not only is he the Spaniards’ best finisher, but he’s a sparkplug with his darting runs and imaginative moves.

His goal came off the kind of attack that has carried Spain toward the top of the soccer world. Andres Iniesta surged through the Paraguay defense and passed to the right to Pedro, whose right-footed kick slammed off the goalpost.

The rebound came to Silva, and his shot hit the far post, then — amazingly — caromed across the net, off the left post and in.

Fans for both teams wore red and blended into the color scheme of the seats in Ellis Park Stadium. Even if you couldn’t see them so well, you sure could hear their vuvuzelas blaring, especially when Silva scored.

But Paraguay, a nation that never has been a factor at the World Cup and hasn’t won a major title since Copa America in 1979, wasn’t about to fold. The final six minutes of regulation and three minutes of extra time featured free-flowing soccer at both ends, and Casillas once again had to rescue the Spaniards.

Lucas Barrios broke free on right wing and Casillas charged out of his net to stop his hard drive. The rebound went to Roque Santa Cruz, and Casillas scrambled back to make a spectacular stop to preserve victory.

At the end, as the Spanish players rushed to mob Casillas, a distraught Cardozo walked away from teammates and team officials, holding his jersey over his face, wiping away tears.

A tournament that belonged to South America for two rounds now has only Uruguay remaining from that continent after Brazil and Argentina also lost in the quarterfinals.

With the likes of Villa, Xavi, Iniesta, Xabi Alonso, Ramos and Fabregas, Spain’s game flows the way Brazil and Argentina have been known to do. It will need all of its creativity and a lot more precision against the Germans, who have scored four goals in three matches and routed England and Argentina in their last two games.

Paraguay’s players couldn’t have been more relaxed before the game, smiling and waving to TV cameras as they came off their bus, then talking on cell phones and joking around on the pitch 90 minutes before kickoff.

The Spaniards were more matter-of-fact, in direct contrast to their playing style. They gathered in a circle and chatted, only occasionally giving a wave to their fans as the stadium began to fill.

Once the match began, Paraguay had Spain off-balance, getting a dangerous scoring chance by Jonathan Santana in the opening minute. Rarely did the Spaniards cross midfield with possession.

But that soon changed as Spain began stringing together passes and dominating possession, looking for a breakthrough. It nearly came on a superb individual effort by Xavi, who took a pass and in one motion, pivoted to send a shot that soared just over the crossbar.

But most of the connections led nowhere, particularly on a dozen set pieces the Spaniards wasted. They left the field after a scoreless first half gesturing at each other in frustration and lucky to be tied at 0-0.

The difference in the frenzied second half were Villa and Casillas.