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.
"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."
"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."
