Slovakia, a central European country of five million people, reached next year's tournament in South Africa after grinding out a nervous 1-0 victory in Poland late on Wednesday.
It was the country's biggest soccer milestone since it emerged as an independent state in 1993 following the peaceful dissolution of its federation with the Czech Republic.
"I had always thought I'd get a heart attack in politics but I was afraid that I'd get one today," Prime Minister Robert Fico, who attended the match in Poland, said afterwards.
Slovakia gave a lacklustre performance in snowy conditions but a third-minute own goal by Polish defender Seweryn Gancarczyk was enough to send them through to the 2010 finals.
"It looked like destiny wanted to tease us fans until the very last seconds of this qualification, I'm still shaking," said 28-year-old Slovakia supporter Michal Dzujko. "This is a tremendous achievement, I still need to take a breath."
Slovakia coach Vladimir Weiss burst into tears after the match, saying he had experienced the greatest joy of his life and the Slovaks deserved their success.
"I've had the toughest three days of this qualification after the loss to Slovenia," the SITA agency quoted Weiss as saying in reference to Saturday's 2-0 home defeat.
"I'm proud of these guys, and I'd like to dedicate this win and qualification to my late mother."
Slovakia finished top of Group Three with 22 points ahead of Slovenia, who reached the playoffs, on 20 and Czech Republic who were eliminated after finishing third with 16 points.
