Slovenia defeated Algeria 1-0 in a Group C match at Polokwane on Sunday to move top of the pool ahead of England and USA.
It was Slovenia's first ever World Cup victory.
The European team took advantage of the red card shown to Abdelkader Ghezzal for a hand ball in the 72nd minutes. Seven minutes later Robert Koren scored the winner after his shot outside the box fooled Algerian goalkeeper Faouzi Chaochi and bounced over his gloves and into the net.
The first-half had offered little in terms of football.