Denmark's unbeaten run in South Africa 2010 qualifying came to an end in Copenhagen at the hands of Hungary and Akos Buzsaky.
Switzerland and Slovakia seized Europe's last two automatic berths in South Africa, while Portugal, Greece, Slovenia and Ukraine made the play-offs.
Switzerland, Greece, Slovakia and Slovenia head into Wednesday's final qualifiers hoping to claim the two remaining direct tickets to South Africa.
Italy, Germany, Denmark and Serbia all sealed their places at South Africa 2010 with positive results during Saturday's nervy round of qualifiers.
Portugal overcame the loss of Cristiano Ronaldo to move into pole position for a South Africa 2010 play-off in their first home win in the campaign.
Ten tickets to South Africa remain up for grabs in Europe, where crucial games are set to unfold in Athens, Copenhagen, Dublin, Lisbon and Moscow.