A first-half goal from Zlatko Dedic earned Slovenia a place at next year's World Cup in South Africa, eliminating Russia on the away goals rule.
Slovenia surprised Russia with its attacking game, giving the visitors little space to play.
Russia won 2-1 in Moscow on Saturday, but Slovenia's 1-0 win in Maribor was enough to secure its berth to South Africa.
"My guys became immortal!" Slovenia coach Matjaz Kek declared.
Defender Bojan Jokic was euphoric: "We were simply better! All of Slovenia is with us!"
Slovenia was the better side from the start and one minute before halftime, Valter Birsa passed the ball to Vfl Bochum striker Dedic, who shot into the left corner of Igor Akinfeev's net.
Slovenia, which gained independence in 1991, played its only previous World Cup in 2002 in South Korea, but lost all three of its matches.
Nervousness seemed to increasingly affect the Russian team as the match went on and Alexander Kerzhakov was red-carded in 66th minute for a foul on Slovenia's goalkeeper Samir Handanovic. Yury Zhirkov was then sent off in the 90th minute for scuffling with Slovenia's reserve players.
Russia's coach Guus Hiddink did not appear as expected at the post-match press conference.
Underlining the importance that both nations attached to the match, Russian President Dmitri Medvedev travelled to Maribor to watch the game alongside his counterpart, Danilo Turk.
Russia's business jet set was also there, including billionaire Chelsea owner Roman Abramovic.
Slovenia pressured Russia from the start and had the first good chance in the fourth minute, when Birsa hit the ball from the penalty area straight to Milivoje Novakovic, who was taken by surprise and fluffed the opportunity.
As the match finished, the crowd of 22,000 — a considerable turnout for a nation of just two million people — erupted in joy as the players performed a victory lap and waved to their fans.
Prime Minister Borut Pahor told Slovenian television he had fulfilled his promise to clean the players' boots if they qualified.
"I didn't do it thoroughly, but enough for the trip to South Africa," Pahor said.